A threshold in a continuous variable determines treatment assignment
Running variable (or “score”), X: a continuously distributed variable with a clearly defined cutoff (c) that determines which units are assigned to treatment and which ones are assigned to control.
Prior to the treatment, the outcome should not differ between the treatment and control group (continuity assumption). The distribution of the variable which indicates the threshold should have no jumps around this cutoff value.
Example using an arbitrary test score cut-off for being enrolled in tutoring programs on learning outcomes, from Andrew Heiss
sharp RDD: the threshold separates the treatment and control group exactly
fuzzy RDD: the threshold influences the probability of being treated. this is in fact an instrumental variable approach (estimating a Local Average Treatment Effect [LATE])
The value of the outcome (Y) for individuals just below the threshold is the missing counterfactual outcome. It increases continuously with the cutoff variable, as opposed to the treatment.
Here are some nice elaborations and fifures on these two variants of RDD from the World Bank
Sharp vs Fuzzy RDD illustration from the World Bank
In fuzzy designs, the probability of treatment is discontinuous at the cutoff, but not to the degree of a definitive 0 to 1 jump. For example, if food stamp eligibility is given to all households below a certain income, but not all households receive the food stamps, then the assignment rule defines treatment status probabilistically but not perfectly. Thus, the design is fuzzy. The fuzziness may result from imperfect compliance with the law/rule/program; imperfect implementation that treated some non-eligible units or neglected to treat some eligible units; spillover effects; or manipulation of the eligibility index.
A fuzzy design assumes that, in the absence of the assignment rule, some of those who take up the treatment would not have participated in the program. The eligibility index acts as a nudge. The subgroup that participates in a program due to the selection rule is called compliers (see e.g. Angrist and Imbens (1994), and Imbens, Angrist, and Rubin (1996)); under the RDD, the treatment effects are estimated only for the group of compliers."
With an RDD approach some assumptions can be tested. Individuals or units close to the threshold are nearly identical, except for characteristics which are affected by the treatment.
RDD’s strengths include that we can:
Load required packages. In this demo, we will use the package “rdrobust”
install.packages("rdrobust",
repos = "http://cran.us.r-project.org")
##
## The downloaded binary packages are in
## /var/folders/_c/txgkq4nd3pqfrsyx1ygqk9kh0000gq/T//RtmpKkJ7LF/downloaded_packages
install.packages("rddensity",
repos = "http://cran.us.r-project.org")
##
## The downloaded binary packages are in
## /var/folders/_c/txgkq4nd3pqfrsyx1ygqk9kh0000gq/T//RtmpKkJ7LF/downloaded_packages
library(tidyverse) # ggplot(), %>%, mutate(), and friends
# library(broom) # Convert models to data frames
library(rdrobust) # For robust nonparametric regression discontinuity
library(rddensity) # For nonparametric regression discontinuity density tests
library(modelsummary) # Create side-by-side regression tables
x<-runif(1000,-1,1) # running variable
y<-5+3*x+2*(x>=0)+rnorm(1000) #outcome with a cut off c at 0
rdrobust(y,x) #apply rdrobust to view sample output
## Call: rdrobust
##
## Number of Obs. 1000
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 502 498
## Eff. Number of Obs. 143 144
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 0.295 0.295
## BW bias (b) 0.508 0.508
## rho (h/b) 0.581 0.581
## Unique Obs. 502 498
We are interested in the causal effect of fishing on crab mortality. This question is surprisingly hard to answer because it’s hard to tease apart natural mortality from fishing mortality, but it is an important effect to estimate for fisheries management.
### Make column for observation ID
crab_data <- data.frame(id = seq(1, 1000),
### Add columns for explanatory variables
### Add column for treatment variable
fished = c(rep(0, 500), rep(1, 500)),
### Add column for body size
size = c(runif(500, min = 10, max = 80),
runif(500, min = 60, max = 130)),
### And the rest of the covariates
sst = runif(1000, min = 10, max = 16),
salinity = runif(1000, min = 1, max = 10),
npp = runif(1000, min = 0, max = 1),
### And the error term
error = rnorm(1000, mean = 0, sd = 2))
### Visualize
ggplot(crab_data) +
geom_boxplot(aes(x = size, group = fished)) +
geom_vline(xintercept = 70)
### center size at legal catch size
crab_data <- crab_data %>%
mutate(size_centered = size - 70)
### Make column for outcome variable (total mortality)
crab_data <- crab_data %>%
mutate(natural_mortality = 10 + -0.4*size_centered + 2*sst + 0.3*npp + 1.5*salinity + error,
fishing_mortality = ifelse(size_centered < 0 & fished == 0,
10 + -0.1*size_centered,
ifelse(size_centered < 0 & fished == 1,
30 + 0.4*size_centered,
ifelse(size_centered > 0 & fished == 0,
10 + -0.1*size_centered,
30 + 0.4*size_centered))),
total_mortality = natural_mortality + fishing_mortality)
### Visualize mortality outcomes
ggplot(crab_data) +
geom_point(aes(x = size_centered,
y = natural_mortality,
color = fished))
ggplot(crab_data) +
geom_point(aes(x = size_centered,
y = fishing_mortality,
color = fished))
ggplot(crab_data) +
geom_point(aes(x = size_centered,
y = total_mortality,
color = fished))
### Visualize covariates
ggplot(crab_data) +
geom_point(aes(x = size_centered,
y = sst,
color = fished))
ggplot(crab_data) +
geom_point(aes(x = size_centered,
y = salinity,
color = fished))
ggplot(crab_data) +
geom_point(aes(x = size_centered,
y = npp,
color = fished))
Example: Rule-based example with cut off: fishing size limits of crabs
In order to be legally harvest, crabs must be larger than 70mm. Crabs smaller than 70mm are not legal to harvest. Harvesting is thus rule-based, according to size. Here, we would probably expect mortality to decline with body size, but the harvest rule changes this relationship at the discontinuity.
Since we know that the program was applied based on a rule, we next want to figure out how strictly the rule was applied (e.g. was there a lot of illegal harvest of crabs that were too small? Were all crabs over 70mm harvested? ).The threshold was 70 mm for legal harvest — e.g., did people who caught crabs that scored 68 mm slip through cracks? The easiest way to check this is with a graph, and we can get exact numbers to verify with a table.
ggplot(crab_data, aes(x = size_centered, y = fishing_mortality, color = fished)) +
# Make points small and semi-transparent since there are lots of them
geom_point(size = 0.5, alpha = 0.5,
position = position_jitter(width = 0, height = 0.25, seed = 1234)) +
# Add vertical line
geom_vline(xintercept = 0) +
# Add labels
labs(x = "Size (centered on 70 as cut-off)", y = "Fished or not") +
# Turn off the color legend, since it's redundant
guides(color = "none")
This discontinuity looks fuzzy rather than sharp We see some evidence of non-compliance around the size-based harvest rules. We will verify in Step 3.
Comparison of Fuzzy vs Sharp Discontinuities from Causal Inference: The MixTape by Cummingham
We next verify our conclusionss from the above visualization that the design is a fuzzy disconintuinity with a table examinging if there crabs under 70 mm harvested, and some over 70mm that weren’t.
crab_data %>%
group_by(fished, size_centered<= 0) %>%
summarize(count = n())
## `summarise()` has grouped output by 'fished'. You can override using the
## `.groups` argument.
## # A tibble: 4 × 3
## # Groups: fished [2]
## fished `size_centered <= 0` count
## <dbl> <lgl> <int>
## 1 0 FALSE 82
## 2 0 TRUE 418
## 3 1 FALSE 437
## 4 1 TRUE 63
Based on the table, we can conclude this is a fuzzy design becuase there are some crabs over the cut-off that were not fished, and some under that were fished.
Next, we need to see if any crabs self selected on either side of the size threshold; this seems unlikely. But, first, we’ll make a histogram of the running variable (size) and see if there are any big jumps around the threshold:
ggplot(crab_data, aes(x = size_centered, fill = fished)) +
geom_histogram(binwidth = 2, color = "white", boundary = 0) +
geom_vline(xintercept = 0) +
labs(x = "Size", y = "Count", fill = "Legal to fish")
## Warning: The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
Here it doesn’t look like there’s a jump around the cutoff. There’s a tiny visible difference between the height of the bars right before and right after the 70-mm sie threshold (centered at 0), but it seems to follow the general shape of the overall distribution.
There’s a fuzzy discontinuity, but how big is it? And is it statistically significant?
This is likely a fuzzy RDD set up: some crabs < 70mm are probably harvested illegally, and fishers are not catching every crab > 70mm. So the treatment assigned is not necessarily the treatment received. To estimate the effect of fishing on total crab mortality in a fuzzy RDD, we take a two stage least squares approach (using a the fuzzy RDD as an IV.
Recall from Session 12 that instruments let us isolate causal effects for just compliers: they let us find the complier average causal effect, or CACE (the effect of a treatment for subjects/units who comply with the experimental treatment assigned to their sample group).
In this case, the instrument is fairly easy and straightforward: we create a variable that indicates if someone is above or below the threshold. That’s all. This variable essentially measures what should have happened rather than what actually happened.
Surprisingly, it meets all the qualifications of an instrument too:
First we will create the IV from the cut-off. We have already centered the running variable (size) on 0, so now we just need to create an indicator variable if the size if above or below 0.
##NEED TO FINISHED
size_centered <- crab_data %>%
mutate(above_cutoff = size_centered >= 0,
below_cutoff = size_centered <= 0)
size_centered
## id fished size sst salinity npp error
## 1 1 0 33.37310 10.59927 3.887024 0.494596675 -1.073614790
## 2 2 0 41.41376 14.76165 5.206678 0.492683967 1.842847368
## 3 3 0 51.62351 11.12562 7.973739 0.487321320 -1.150183228
## 4 4 0 39.96777 15.33336 5.004385 0.680442168 -0.767621241
## 5 5 0 38.48896 12.75092 3.002153 0.119928838 -2.464746073
## 6 6 0 54.16535 10.72544 6.811565 0.421503302 -2.056298479
## 7 7 0 74.16030 13.38142 4.489062 0.281738795 0.084957871
## 8 8 0 64.69715 14.61249 2.781528 0.526460395 0.268678090
## 9 9 0 41.80104 13.02843 6.640495 0.294976354 3.320008667
## 10 10 0 19.90219 13.01592 4.135263 0.575951713 0.146680062
## 11 11 0 25.72918 11.94644 1.564524 0.916633083 0.119128951
## 12 12 0 74.17120 13.71824 3.096980 0.973887147 -2.011411746
## 13 13 0 16.39916 15.46050 5.053012 0.204417424 -0.092828793
## 14 14 0 52.13472 15.88613 2.097055 0.584458308 3.469534927
## 15 15 0 27.15036 14.65409 9.476714 0.897742154 2.536128422
## 16 16 0 69.70959 11.44734 3.152656 0.509893499 -0.435135470
## 17 17 0 47.44967 11.37143 3.030767 0.240254555 0.972488359
## 18 18 0 12.94942 13.41042 6.592244 0.971215750 -3.392684813
## 19 19 0 21.08850 15.59445 1.716652 0.827355800 1.473752951
## 20 20 0 43.68907 14.03203 3.104641 0.919271898 2.374906447
## 21 21 0 49.27901 14.69721 5.103537 0.688269655 2.981330814
## 22 22 0 77.20233 10.36719 1.905043 0.402658348 -2.156394649
## 23 23 0 75.82050 10.38967 6.414845 0.751740434 1.754465156
## 24 24 0 37.92843 11.79126 1.028065 0.729490436 2.283081084
## 25 25 0 65.85707 13.73250 2.568082 0.810565792 2.245472442
## 26 26 0 20.73500 15.04458 8.030145 0.305577752 1.305043084
## 27 27 0 75.62863 10.55658 1.641082 0.295610174 2.690527344
## 28 28 0 66.32443 12.35095 3.595475 0.061130400 3.637177230
## 29 29 0 38.71703 15.38567 3.028464 0.466630139 0.681023972
## 30 30 0 19.68255 14.96014 8.759834 0.909825013 -0.316410136
## 31 31 0 44.06650 11.03813 2.116915 0.251121590 4.318064057
## 32 32 0 60.80977 14.58397 9.145512 0.241336541 3.246976808
## 33 33 0 61.13586 12.28360 8.056790 0.351188044 -2.040257663
## 34 34 0 12.37440 13.73760 5.519380 0.746217108 -1.775852977
## 35 35 0 14.05561 15.12592 7.386041 0.674171328 -0.021853185
## 36 36 0 70.77356 13.77019 3.963972 0.127754140 -2.792951737
## 37 37 0 27.09370 14.61036 6.617635 0.774869803 1.339523037
## 38 38 0 29.23035 10.48532 7.256270 0.244572551 -0.377570183
## 39 39 0 63.11804 15.69887 5.395231 0.468912730 1.374590215
## 40 40 0 25.83693 11.82498 3.384566 0.302259645 -1.880109058
## 41 41 0 13.87111 12.27457 8.750711 0.951705037 -2.804488578
## 42 42 0 12.48936 14.07721 4.994538 0.431387697 -0.988109064
## 43 43 0 43.19683 13.39142 5.813704 0.249399324 3.079072235
## 44 44 0 46.59476 11.02856 3.579972 0.413850058 1.109878199
## 45 45 0 16.06293 15.30256 8.724323 0.520869543 -1.304714360
## 46 46 0 64.19618 15.37798 4.880369 0.758276488 -0.547479415
## 47 47 0 66.52012 15.52607 4.803162 0.772996419 1.077692649
## 48 48 0 36.28493 15.18486 7.415118 0.257804012 0.253193271
## 49 49 0 74.23490 10.86472 5.322908 0.698600599 2.164984112
## 50 50 0 67.23035 10.90189 9.523228 0.987741726 4.530373347
## 51 51 0 36.37309 15.37575 9.074279 0.515469426 4.348085366
## 52 52 0 11.92205 11.89925 8.546083 0.354368949 3.070311258
## 53 53 0 71.17861 12.40579 3.648319 0.441485061 -2.150947687
## 54 54 0 23.25916 14.16284 3.263267 0.600542699 -1.776892170
## 55 55 0 51.11880 13.10782 9.560309 0.975718399 0.399962158
## 56 56 0 25.47797 15.74108 2.187035 0.321954943 -3.181568129
## 57 57 0 13.92030 10.88714 7.978228 0.292232560 -0.431999740
## 58 58 0 75.37467 14.80403 9.518592 0.197831195 2.195268021
## 59 59 0 47.92665 14.15736 9.994849 0.866407647 1.024548009
## 60 60 0 12.87387 14.32639 1.436245 0.869400671 -1.255628977
## 61 61 0 31.97767 10.94018 6.969154 0.357436004 -1.284833273
## 62 62 0 64.99726 12.81974 2.756903 0.164609042 -1.532447205
## 63 63 0 46.19775 13.99349 2.522038 0.622985227 1.945550088
## 64 64 0 60.36406 15.95188 5.602029 0.294745947 1.565621091
## 65 65 0 42.11466 15.80957 8.432459 0.813238875 -0.522785163
## 66 66 0 69.07083 14.98427 8.766221 0.283023220 0.004624792
## 67 67 0 12.02701 14.81057 9.922681 0.784318202 0.589750666
## 68 68 0 27.21351 12.16373 2.179820 0.863419081 3.071398308
## 69 69 0 49.43366 13.87355 4.069447 0.511862504 -5.584350659
## 70 70 0 18.61745 15.76411 3.249029 0.650089623 -2.062714285
## 71 71 0 71.88315 11.98593 2.668217 0.177248153 0.520961636
## 72 72 0 73.15826 13.87524 7.766180 0.768716742 0.289615917
## 73 73 0 26.18027 11.72852 6.109876 0.522584254 2.535256856
## 74 74 0 12.26033 14.94655 3.870162 0.990094313 -2.312723554
## 75 75 0 27.73463 15.68789 8.980212 0.479579740 -0.488648754
## 76 76 0 36.69774 14.27316 8.528913 0.750989122 -1.478070010
## 77 77 0 77.83635 14.27551 6.805031 0.659488135 2.339661849
## 78 78 0 66.27114 11.33931 5.085159 0.726599531 -1.732131332
## 79 79 0 20.94700 10.07947 6.996821 0.014302273 0.019519622
## 80 80 0 27.60740 14.30717 8.925224 0.076955062 0.762314449
## 81 81 0 59.86536 12.52449 4.784308 0.770116679 1.025635939
## 82 82 0 14.32249 11.83245 7.345967 0.926316587 -1.775175849
## 83 83 0 57.94736 13.67874 2.100912 0.904102330 0.218773280
## 84 84 0 77.11781 11.63143 8.136935 0.790796537 0.656035849
## 85 85 0 10.13398 12.61578 8.731368 0.764309913 0.342912428
## 86 86 0 36.64132 10.77696 3.587292 0.951976947 1.104377451
## 87 87 0 38.97021 13.46027 9.142175 0.676645987 0.920668512
## 88 88 0 63.24388 14.86026 2.223349 0.378872704 4.164443202
## 89 89 0 37.93457 11.30461 8.641627 0.030429876 -1.044644063
## 90 90 0 28.66860 12.64767 9.682197 0.902427718 0.285185985
## 91 91 0 29.61235 14.53405 8.029733 0.094295227 -4.192061480
## 92 92 0 15.37892 13.48581 4.877622 0.182142639 0.113833825
## 93 93 0 24.65556 13.06647 5.855784 0.792670486 2.231774653
## 94 94 0 60.88257 15.01456 8.832034 0.586692832 -3.496206099
## 95 95 0 43.69759 11.23137 7.986527 0.264909068 -1.359946808
## 96 96 0 17.88836 15.29865 9.914078 0.815960316 -0.643685532
## 97 97 0 65.98527 14.63569 8.735918 0.974536126 1.874956314
## 98 98 0 17.04179 14.32140 2.726958 0.558466529 -0.420152830
## 99 99 0 75.20136 12.28832 8.465133 0.418911049 -3.622802907
## 100 100 0 73.26023 12.55857 3.035576 0.716546475 -0.489421911
## 101 101 0 42.05973 11.98217 2.893860 0.028887988 1.251864277
## 102 102 0 16.53942 11.57621 1.381403 0.758359779 0.208415505
## 103 103 0 25.15308 11.21432 8.773388 0.915596707 -2.033982867
## 104 104 0 44.83964 15.48664 6.312367 0.544482537 -5.643629772
## 105 105 0 46.69616 12.25478 2.701779 0.033052348 1.809515215
## 106 106 0 39.22486 12.98355 9.713968 0.800321290 1.819143909
## 107 107 0 40.76099 12.82462 7.803460 0.540951464 -3.287322085
## 108 108 0 43.75537 13.91665 5.853926 0.815857556 -3.031226804
## 109 109 0 63.09848 15.94103 7.951839 0.486443270 -0.989115730
## 110 110 0 53.83185 11.95210 3.783016 0.143505742 -1.129135480
## 111 111 0 25.94164 15.92858 7.452694 0.612250604 -1.481500784
## 112 112 0 38.91129 12.63588 1.011004 0.624500828 -2.791958189
## 113 113 0 70.66383 10.41061 5.861048 0.071132711 0.264732414
## 114 114 0 54.26053 10.64339 9.629680 0.148267430 -1.266253659
## 115 115 0 77.24640 10.62828 9.773420 0.912052301 2.178884062
## 116 116 0 32.30771 13.45395 1.244513 0.799894103 -1.463932103
## 117 117 0 46.25095 10.22329 2.239068 0.298696314 5.090604858
## 118 118 0 64.68883 10.29096 9.558756 0.341365145 -0.078170343
## 119 119 0 69.23720 13.58166 9.013647 0.211115374 -1.672705385
## 120 120 0 31.81627 15.99567 7.025038 0.816575342 0.764453202
## 121 121 0 47.36487 13.66874 9.055389 0.973902941 0.926559968
## 122 122 0 71.86791 11.85501 3.038448 0.266165299 -1.594563186
## 123 123 0 26.76832 12.21446 4.888050 0.294325066 -0.749292791
## 124 124 0 58.95658 15.02226 4.056528 0.040936453 2.480414991
## 125 125 0 60.03132 11.77063 6.940378 0.852810399 -1.059344630
## 126 126 0 13.95451 11.62312 2.154888 0.565934502 1.889018113
## 127 127 0 28.84147 11.09523 4.123034 0.314001128 0.348941195
## 128 128 0 55.75212 15.55009 5.938676 0.979489752 1.042588444
## 129 129 0 46.83145 11.27260 4.468514 0.828551237 -1.274033141
## 130 130 0 24.40523 14.41496 6.835154 0.945057308 2.470234709
## 131 131 0 51.66827 10.54242 3.225351 0.806369240 0.955288778
## 132 132 0 16.95237 15.87858 8.397524 0.564503106 0.632548429
## 133 133 0 79.07235 13.99796 4.254142 0.081295379 -0.655904963
## 134 134 0 44.54745 12.41741 5.741543 0.027816274 -0.082001955
## 135 135 0 69.51286 13.25732 8.880052 0.804284972 0.337911871
## 136 136 0 28.16767 14.47184 5.470873 0.339890615 -0.951201791
## 137 137 0 28.79018 11.44484 4.202270 0.707534101 0.039293264
## 138 138 0 71.68404 11.75096 1.812905 0.372201980 1.316052720
## 139 139 0 30.71370 13.89438 1.028186 0.917771715 -4.139183831
## 140 140 0 44.23557 15.10428 8.745734 0.595391935 1.983561437
## 141 141 0 73.50580 10.01707 2.133852 0.343188161 -1.729519035
## 142 142 0 36.39898 13.16604 6.836956 0.292859078 3.183761922
## 143 143 0 44.91613 15.26486 9.023531 0.124183269 2.626251542
## 144 144 0 49.09474 13.64410 2.497706 0.035986973 -1.087021277
## 145 145 0 40.68214 13.44009 1.093051 0.315904814 -1.517870656
## 146 146 0 19.58231 11.55007 8.084393 0.241312585 2.591921127
## 147 147 0 57.34401 15.24146 6.744282 0.743340578 1.368647866
## 148 148 0 64.79597 14.14911 4.924699 0.226645124 4.018198511
## 149 149 0 69.08698 13.01636 6.003417 0.672652120 2.764846229
## 150 150 0 53.95742 14.03821 5.548458 0.367899386 0.146979375
## 151 151 0 41.00902 15.37712 7.520179 0.699607499 -0.340104355
## 152 152 0 41.87358 10.37151 3.408129 0.979655558 1.165883476
## 153 153 0 23.85389 15.23508 5.820680 0.660290791 0.317356214
## 154 154 0 17.45317 11.41321 6.137282 0.662288752 1.343028205
## 155 155 0 44.00323 15.01857 7.575310 0.370675190 2.652168472
## 156 156 0 30.47307 11.55816 1.671206 0.711181426 0.113372009
## 157 157 0 28.88146 12.05573 5.193916 0.896854685 -3.267953955
## 158 158 0 76.33200 12.38293 9.430888 0.533550434 -4.077842193
## 159 159 0 28.47558 10.38157 6.990518 0.767701208 3.159910747
## 160 160 0 53.38135 13.05286 9.108600 0.146378411 -1.433184685
## 161 161 0 75.04453 12.54900 2.260060 0.525627737 0.029146140
## 162 162 0 31.45929 11.39528 2.870752 0.633271806 -1.786032240
## 163 163 0 75.02236 14.47372 4.156191 0.929155299 -1.070414613
## 164 164 0 49.98972 13.11023 9.754803 0.645515413 -2.989300072
## 165 165 0 60.76561 15.03285 6.556543 0.942639516 1.334546012
## 166 166 0 61.18351 14.49652 5.144049 0.847628968 1.262754029
## 167 167 0 47.87352 11.53326 5.258863 0.722662852 3.669380779
## 168 168 0 75.87447 11.11850 4.700712 0.922042788 1.544426483
## 169 169 0 28.82695 14.94294 5.412934 0.918613423 1.864874353
## 170 170 0 50.43793 12.24744 7.582546 0.802254211 -0.029269879
## 171 171 0 67.97148 15.71199 1.498966 0.803063539 -1.634882044
## 172 172 0 19.71108 10.44356 1.425048 0.175289435 -1.618919531
## 173 173 0 66.96493 13.96047 1.977237 0.564451003 -2.661452182
## 174 174 0 79.80876 15.69305 5.798535 0.733624438 0.513653312
## 175 175 0 43.40280 11.20970 1.031668 0.146442496 -2.544886619
## 176 176 0 72.78180 13.74182 2.621612 0.564606054 -2.700000553
## 177 177 0 55.55187 10.91288 3.424849 0.378678552 -0.100296319
## 178 178 0 37.40167 14.43993 1.072569 0.792392365 0.131526388
## 179 179 0 18.90092 10.98776 3.138443 0.201364568 2.493000735
## 180 180 0 50.30639 14.63954 1.389474 0.352370405 1.565819362
## 181 181 0 58.37656 13.88133 2.150042 0.566594328 -1.752533576
## 182 182 0 67.51871 12.63140 3.137261 0.707538600 -2.238613459
## 183 183 0 20.22278 15.07362 5.760287 0.592988458 1.789320406
## 184 184 0 70.70071 11.72522 8.280884 0.828490654 -2.303988067
## 185 185 0 53.29235 13.73962 2.848845 0.296104416 -0.209290108
## 186 186 0 27.80259 11.08513 6.693874 0.112026764 -0.032399957
## 187 187 0 71.31880 14.78138 9.959894 0.729622530 -2.611032066
## 188 188 0 21.45910 14.76405 2.945389 0.180188484 -0.086372714
## 189 189 0 11.70622 15.37385 1.806424 0.625180312 1.419522858
## 190 190 0 56.92235 10.00408 4.825135 0.338130000 0.713367927
## 191 191 0 76.13104 11.16113 7.055637 0.027280151 -1.596799533
## 192 192 0 74.21456 12.71690 3.802008 0.320207546 -2.054733266
## 193 193 0 19.59262 14.19287 2.746683 0.720457340 -0.813765453
## 194 194 0 36.73329 12.44507 4.189601 0.781347777 2.317476546
## 195 195 0 63.66214 11.52241 4.362642 0.083523411 2.762040820
## 196 196 0 78.44567 12.36565 8.897275 0.064666453 2.978258053
## 197 197 0 15.81907 11.33143 2.821123 0.754580904 1.016229829
## 198 198 0 76.08652 11.73820 4.870334 0.631629198 1.744944600
## 199 199 0 31.23073 11.81419 3.509870 0.631726432 0.543946802
## 200 200 0 59.10610 10.55321 3.870847 0.220622243 -1.509800067
## 201 201 0 40.31863 15.57033 8.303550 0.998299149 -1.808046350
## 202 202 0 76.96226 11.97265 6.044343 0.985808577 1.734974005
## 203 203 0 59.93581 11.56778 8.526474 0.881453090 -4.529958394
## 204 204 0 15.72896 12.43392 3.769447 0.160212963 0.167652177
## 205 205 0 46.61364 14.77801 3.965770 0.936863089 2.219691218
## 206 206 0 68.86406 13.81320 5.672729 0.787372121 0.687777296
## 207 207 0 30.28370 13.09745 6.749696 0.103580133 -3.125680626
## 208 208 0 23.89488 11.00652 9.307598 0.161540650 -0.936799607
## 209 209 0 70.29540 11.63531 2.614578 0.445740753 0.060873098
## 210 210 0 63.82159 12.88531 5.518052 0.563378881 0.450199201
## 211 211 0 21.56700 12.48634 6.391390 0.659591349 3.246506984
## 212 212 0 26.64370 15.91677 3.441875 0.823806694 0.263306993
## 213 213 0 48.67881 11.26490 4.486115 0.412615071 -0.430131381
## 214 214 0 57.01544 15.50228 7.223225 0.565507163 0.100596793
## 215 215 0 46.89771 13.24805 1.968387 0.124943918 -2.196325232
## 216 216 0 65.46856 13.95376 1.940125 0.268819745 -1.288300624
## 217 217 0 22.42616 15.75658 8.071102 0.630284558 -1.863486751
## 218 218 0 25.50486 10.20965 4.756560 0.913943380 0.912372961
## 219 219 0 29.96744 13.88616 6.270915 0.626851060 0.465497352
## 220 220 0 78.10638 15.32039 7.730089 0.106426144 1.507955643
## 221 221 0 40.00163 11.92891 3.140213 0.213127193 1.220706651
## 222 222 0 28.57338 14.11748 4.079059 0.978862273 -0.426815607
## 223 223 0 77.90757 15.32256 8.732507 0.501020048 2.970636633
## 224 224 0 66.56684 10.45010 2.558891 0.313060647 2.015285762
## 225 225 0 27.44429 15.82896 2.751678 0.425702267 -1.342789524
## 226 226 0 56.79356 14.76828 5.186140 0.700650075 -1.048769393
## 227 227 0 13.50754 12.31604 5.939399 0.658521382 0.291686197
## 228 228 0 38.73624 10.27145 9.340725 0.271584277 1.613474583
## 229 229 0 24.85324 14.50066 1.197655 0.953933537 1.462021969
## 230 230 0 43.43103 14.50792 7.725480 0.165115024 2.393059727
## 231 231 0 75.91700 13.74523 9.103160 0.679240661 2.641452735
## 232 232 0 59.57601 13.73142 8.772134 0.903762000 -1.443723451
## 233 233 0 37.30042 14.01062 2.750291 0.115129182 1.279721428
## 234 234 0 23.07195 13.90242 7.669261 0.914934525 1.278924659
## 235 235 0 66.54842 11.60874 2.389795 0.070607719 2.843552051
## 236 236 0 22.78810 14.17363 6.244069 0.109838545 2.110651216
## 237 237 0 66.90382 14.94799 6.714474 0.782704561 0.099079869
## 238 238 0 54.89205 11.49839 6.302524 0.244112006 1.826933493
## 239 239 0 21.55764 12.19913 6.579803 0.733279373 0.999736475
## 240 240 0 41.19324 11.67669 7.788884 0.744644769 0.388161097
## 241 241 0 77.03632 10.37834 1.513292 0.493009630 -0.247635114
## 242 242 0 73.52655 11.53975 6.888733 0.062175275 -3.278575883
## 243 243 0 18.38243 10.64355 8.342553 0.865691980 -1.526387430
## 244 244 0 65.23560 11.66450 9.894647 0.125771259 0.411748868
## 245 245 0 52.24073 14.41614 1.791946 0.174186372 -2.329782979
## 246 246 0 26.68661 11.59309 1.749363 0.317250385 0.900945622
## 247 247 0 35.18507 11.67338 1.703804 0.848967103 -0.362268961
## 248 248 0 79.52727 14.92435 2.860309 0.099299040 -3.918760125
## 249 249 0 46.06591 11.34013 3.635658 0.284280707 -0.135431227
## 250 250 0 26.55932 11.29264 5.662438 0.904877696 1.782028628
## 251 251 0 55.75768 14.82242 6.285836 0.437849965 0.169624828
## 252 252 0 37.64078 15.41116 2.556505 0.299891629 2.172172846
## 253 253 0 46.57544 15.86493 3.284899 0.348055907 1.127582712
## 254 254 0 52.60212 11.62509 8.050945 0.816747312 0.168460509
## 255 255 0 52.14878 13.71282 9.165545 0.340840983 2.116380661
## 256 256 0 42.46955 12.82898 4.542120 0.974124033 4.148481729
## 257 257 0 45.44774 10.46914 5.063449 0.408129274 1.249826581
## 258 258 0 14.12920 12.95948 1.239462 0.023525185 -1.260255191
## 259 259 0 36.47464 12.39134 1.055387 0.260387609 -2.812280814
## 260 260 0 75.21385 12.68873 6.041716 0.866354606 -1.531934782
## 261 261 0 66.29012 14.67365 9.328269 0.457811426 0.682283689
## 262 262 0 37.73699 14.22277 3.196831 0.173683174 1.196918390
## 263 263 0 71.81161 10.14475 3.297854 0.434726230 -1.938546912
## 264 264 0 66.50925 13.37133 9.229939 0.579171791 5.128667939
## 265 265 0 51.92934 13.15772 3.180458 0.508816044 -1.106167667
## 266 266 0 27.60525 15.80116 6.375459 0.140830521 3.237204866
## 267 267 0 10.46816 15.57644 2.153762 0.535359893 1.285901627
## 268 268 0 51.59797 15.47401 3.976983 0.503699793 3.757529035
## 269 269 0 51.25726 14.56972 6.687326 0.694173704 -0.920237934
## 270 270 0 67.20840 12.93476 7.316381 0.628476985 2.206969495
## 271 271 0 76.45757 11.98053 3.662515 0.422693877 0.150306411
## 272 272 0 55.61186 12.33810 5.443158 0.996445293 0.843983264
## 273 273 0 37.79962 10.71214 4.938019 0.379250377 2.244267691
## 274 274 0 37.01699 12.15424 5.113778 0.563166864 2.267325159
## 275 275 0 33.84054 11.67348 5.768696 0.316238095 -0.829414065
## 276 276 0 35.50911 13.93726 1.701843 0.862734178 -1.512151473
## 277 277 0 67.78639 11.93774 7.288323 0.081971800 1.632035266
## 278 278 0 11.65598 11.04341 6.911189 0.736006772 1.353829026
## 279 279 0 54.04731 14.15300 1.664372 0.903604408 -2.090783992
## 280 280 0 56.91664 12.23982 6.916735 0.420500766 -3.333837598
## 281 281 0 57.53562 12.62240 2.949079 0.989919636 -0.245622138
## 282 282 0 49.58939 15.54253 3.942430 0.228934414 1.950163200
## 283 283 0 24.48846 12.26786 5.454755 0.473918537 -1.161431749
## 284 284 0 49.50905 14.91951 1.315489 0.185543334 1.894874182
## 285 285 0 14.78282 12.97814 1.685209 0.432098322 2.396864542
## 286 286 0 52.01691 14.23457 7.932695 0.707294224 -1.851175463
## 287 287 0 79.11526 12.66566 3.983109 0.479497917 0.507713120
## 288 288 0 55.94852 10.82308 8.754099 0.700933954 0.117807023
## 289 289 0 60.27866 10.79267 7.076755 0.348269003 0.095016190
## 290 290 0 28.56987 12.54587 5.413241 0.987915599 0.380264063
## 291 291 0 74.92847 14.88439 7.392595 0.593889618 -1.528328867
## 292 292 0 73.13637 14.21225 3.633757 0.674694530 -0.424679232
## 293 293 0 41.48972 15.23865 8.027464 0.294039258 -0.669514719
## 294 294 0 74.93994 11.50212 5.388035 0.871416920 1.800837326
## 295 295 0 76.07015 13.41099 2.000335 0.049711701 0.605780517
## 296 296 0 40.54934 14.65628 5.635648 0.564841594 3.692310474
## 297 297 0 79.59201 10.98926 9.652310 0.711131857 -1.131239303
## 298 298 0 35.97555 13.72281 4.918713 0.967307272 -1.554081302
## 299 299 0 33.07444 11.62409 9.977899 0.292672571 3.321840951
## 300 300 0 38.31559 14.23190 6.834339 0.509650384 -0.125533149
## 301 301 0 31.40237 10.24217 4.819343 0.906310339 -3.845145090
## 302 302 0 54.09476 10.95468 6.923302 0.798366922 -2.161833398
## 303 303 0 46.97420 12.94024 3.350847 0.345429444 0.676549948
## 304 304 0 76.42504 11.83967 9.301007 0.078606379 -2.071297148
## 305 305 0 18.35085 10.02154 4.743754 0.281916371 -1.925571044
## 306 306 0 47.17215 11.46597 5.502248 0.170375858 -1.362728473
## 307 307 0 36.23041 15.81549 4.600969 0.273167222 1.861672183
## 308 308 0 72.90273 10.00525 3.220888 0.251615859 3.702163957
## 309 309 0 15.13093 10.74388 7.263263 0.963644451 -0.775649245
## 310 310 0 74.16748 11.77547 2.258090 0.166247873 -0.618500488
## 311 311 0 10.10135 10.12171 7.282005 0.135516140 -4.320182407
## 312 312 0 79.80301 12.29750 7.400945 0.069610425 3.437474296
## 313 313 0 35.19331 13.27804 7.219781 0.183219942 1.771461674
## 314 314 0 57.89854 11.88238 8.153333 0.550580321 -1.525710518
## 315 315 0 47.11534 13.53050 1.497813 0.564053546 -0.145379056
## 316 316 0 25.59193 13.56553 5.356951 0.354642802 1.119889350
## 317 317 0 14.57563 10.65990 7.506856 0.239255951 2.193858999
## 318 318 0 20.99038 14.49182 8.482911 0.984806948 -0.319214728
## 319 319 0 30.29986 15.78368 2.547947 0.334053014 -2.862390849
## 320 320 0 77.88606 15.79060 1.331332 0.700502835 -3.642790176
## 321 321 0 52.81010 14.01878 9.007116 0.046600636 -2.313918588
## 322 322 0 47.09636 12.52877 8.961923 0.119605783 -3.686845131
## 323 323 0 67.49568 12.87963 1.438380 0.011609182 -0.076261131
## 324 324 0 37.51417 15.18867 6.122803 0.840523319 -1.592872732
## 325 325 0 49.12895 15.29381 6.828086 0.583998392 1.556412223
## 326 326 0 39.75892 12.65537 1.308841 0.476118835 -2.458617328
## 327 327 0 58.85526 15.23915 2.654050 0.113355148 0.077500863
## 328 328 0 61.03344 10.91010 6.966537 0.291404719 -0.487888596
## 329 329 0 40.33636 15.08978 9.550083 0.591600812 2.773493537
## 330 330 0 22.61428 12.17060 7.643242 0.705368194 4.668296070
## 331 331 0 41.54062 13.85169 2.221575 0.067522590 -4.662877952
## 332 332 0 31.29018 10.79601 4.535968 0.114091226 0.840816064
## 333 333 0 60.98901 11.27934 1.428409 0.547951514 0.195036653
## 334 334 0 46.05285 14.68161 1.297102 0.501943247 -3.561793893
## 335 335 0 57.91023 11.57250 3.592990 0.135333540 -1.879403266
## 336 336 0 11.14023 14.90260 4.131755 0.792456165 -0.621335850
## 337 337 0 59.21256 15.34562 9.094749 0.192714785 -0.332495942
## 338 338 0 62.85262 12.39101 7.177869 0.357598829 2.298635924
## 339 339 0 64.80772 12.61406 5.601512 0.416484439 -1.678711093
## 340 340 0 66.57977 12.27946 4.282340 0.599660745 2.069628838
## 341 341 0 48.21908 10.36068 6.834804 0.743605861 1.306284478
## 342 342 0 56.16547 11.12928 2.209245 0.039999695 0.470887061
## 343 343 0 20.52158 11.61492 1.608158 0.858430199 1.025888720
## 344 344 0 41.10567 14.60525 4.511541 0.430584218 -2.797730076
## 345 345 0 44.11010 12.60227 1.920573 0.188201864 -3.623984868
## 346 346 0 76.28201 15.30625 2.026724 0.261430226 -4.277084129
## 347 347 0 66.91505 11.97937 1.377518 0.854329573 1.664594046
## 348 348 0 45.31870 14.13358 7.139068 0.084470250 -3.064708587
## 349 349 0 11.02316 12.82651 8.865534 0.770503413 -1.297047510
## 350 350 0 40.90840 15.05980 3.887900 0.027562850 -0.742123952
## 351 351 0 61.73969 15.56404 2.309854 0.722906907 0.779341442
## 352 352 0 31.02340 10.00324 9.187531 0.360918917 1.635017942
## 353 353 0 62.30343 12.32077 2.048490 0.357509851 3.201057784
## 354 354 0 62.35872 13.72809 8.885294 0.624784651 0.237643237
## 355 355 0 15.79277 14.96551 4.338136 0.812201337 -1.071790665
## 356 356 0 28.32050 11.64002 8.501668 0.195537815 -2.559917259
## 357 357 0 12.80881 13.50887 7.068706 0.596623966 -0.873846230
## 358 358 0 18.68231 10.67802 6.598852 0.498026164 -0.055879885
## 359 359 0 61.87716 11.63985 8.907720 0.120424772 2.786273806
## 360 360 0 45.77652 11.46294 4.198947 0.593324346 1.006053972
## 361 361 0 24.39431 14.83260 6.413530 0.438778059 3.101302682
## 362 362 0 24.36346 10.73254 9.700002 0.623549878 -1.788450409
## 363 363 0 25.50300 13.53461 8.286810 0.627634437 -0.134290009
## 364 364 0 40.73393 15.54154 5.035705 0.138558608 -2.100553246
## 365 365 0 34.59409 15.69473 8.616754 0.637339296 -1.795184115
## 366 366 0 22.62083 10.08567 3.861635 0.346635636 1.224793953
## 367 367 0 27.91125 11.96933 2.134880 0.143564355 -3.106608729
## 368 368 0 30.99211 11.87581 4.674868 0.325149701 0.757626991
## 369 369 0 64.30438 11.93617 6.296815 0.100725546 -4.379288479
## 370 370 0 67.75398 15.39552 7.124523 0.021317158 1.328038911
## 371 371 0 74.84444 14.42319 2.332006 0.261976593 0.703190840
## 372 372 0 60.36838 10.42344 5.934303 0.094930030 1.374463250
## 373 373 0 55.53085 11.52427 9.100810 0.183179804 -3.578914585
## 374 374 0 27.17614 12.54802 9.081595 0.977158589 3.694738067
## 375 375 0 79.76175 13.97977 3.484129 0.631162328 -3.155881000
## 376 376 0 66.44929 14.34790 1.978717 0.043292703 -0.430024966
## 377 377 0 38.93744 13.23568 1.791522 0.322480845 0.448590692
## 378 378 0 35.66485 11.59185 7.672887 0.114719687 -1.855558729
## 379 379 0 38.29131 12.21905 5.176548 0.384148553 0.090364581
## 380 380 0 14.93573 15.69266 8.422685 0.038092417 -2.727505531
## 381 381 0 60.02705 12.35447 9.011425 0.531412574 0.438808910
## 382 382 0 55.80625 11.09505 9.746703 0.357942035 0.984272181
## 383 383 0 42.23635 12.60649 9.256905 0.609194689 -0.309585652
## 384 384 0 61.61325 12.66639 1.428402 0.122823809 1.587781962
## 385 385 0 36.54355 12.17845 7.146418 0.466838249 2.155721388
## 386 386 0 45.66845 12.62271 7.468700 0.231174840 3.041112312
## 387 387 0 75.43449 13.80491 3.169636 0.988880865 -4.265641899
## 388 388 0 57.97498 14.00407 5.439856 0.183497970 2.389069640
## 389 389 0 16.58439 12.12109 6.904335 0.004592668 -1.695159481
## 390 390 0 29.34349 11.52012 8.876113 0.206136626 -0.826494335
## 391 391 0 59.93914 12.72481 8.960705 0.574374454 -4.641294329
## 392 392 0 49.34955 12.91799 6.009359 0.156798044 0.624775697
## 393 393 0 40.71054 15.39895 7.575792 0.785529592 2.786752591
## 394 394 0 31.02149 14.39653 7.627913 0.188225026 2.881158349
## 395 395 0 25.72459 11.52970 1.677692 0.599573665 -0.402266772
## 396 396 0 79.01091 13.64082 3.918149 0.949652760 -0.371671492
## 397 397 0 20.52129 12.15753 2.105225 0.883754080 2.193449220
## 398 398 0 16.10429 14.71220 4.036390 0.726904152 0.704144278
## 399 399 0 66.19587 15.11398 6.322207 0.764371166 -1.086724303
## 400 400 0 30.14803 12.05470 2.322738 0.049622783 -3.208141917
## 401 401 0 48.64880 13.93406 8.960797 0.471114014 1.644699670
## 402 402 0 74.18884 14.42333 9.670613 0.209059123 -1.747673955
## 403 403 0 77.28147 10.23882 3.209177 0.996699156 2.321923528
## 404 404 0 73.64180 11.67407 1.888203 0.115296102 1.710142250
## 405 405 0 28.47692 15.40512 8.883600 0.215135565 -1.405606806
## 406 406 0 50.89501 11.00258 5.011919 0.057418960 1.204107078
## 407 407 0 20.30261 13.61400 3.246284 0.388872994 0.766705856
## 408 408 0 13.13903 14.22943 1.080510 0.336790988 1.745946131
## 409 409 0 51.64684 14.63265 8.798376 0.737869869 2.512492402
## 410 410 0 53.55931 14.73616 9.878112 0.010183791 -1.091658800
## 411 411 0 32.54231 13.64795 6.375715 0.765458696 -2.376192388
## 412 412 0 54.74182 13.00167 8.312435 0.748293975 -2.499717409
## 413 413 0 40.41622 11.52543 1.589100 0.473813273 0.705646348
## 414 414 0 52.81326 10.22180 6.624250 0.276103804 0.146287143
## 415 415 0 26.47039 14.51979 5.416370 0.940606884 0.959106255
## 416 416 0 39.38440 10.35643 1.212599 0.925908485 0.659348134
## 417 417 0 46.02137 10.07010 3.622698 0.648214367 1.074051446
## 418 418 0 20.92300 12.09343 3.787904 0.948616337 4.325867051
## 419 419 0 29.10737 14.91165 8.477723 0.558333712 0.384311133
## 420 420 0 61.89565 14.57820 2.482310 0.850618929 -1.774537372
## 421 421 0 62.95618 13.66329 6.384703 0.558570524 3.901671010
## 422 422 0 70.04591 11.92358 7.041287 0.651439219 -0.637115170
## 423 423 0 63.28079 13.30145 4.668653 0.174675365 -1.611973173
## 424 424 0 79.96402 10.37368 5.031956 0.078792606 0.430637560
## 425 425 0 43.38596 15.02212 3.179875 0.549459375 -2.364912352
## 426 426 0 15.28933 10.83186 6.667563 0.468603011 -0.185929581
## 427 427 0 40.72771 15.40827 2.671683 0.732077773 -1.843659660
## 428 428 0 34.64193 10.78302 9.537024 0.607795965 -0.219501015
## 429 429 0 60.71692 12.91494 4.008034 0.114555355 3.359991740
## 430 430 0 64.72333 13.69236 1.027972 0.301706112 0.269325901
## 431 431 0 79.13657 10.44787 5.591979 0.345200806 -2.398388658
## 432 432 0 79.51190 13.24166 2.050861 0.881751652 0.233378236
## 433 433 0 78.91863 12.52914 3.904363 0.423076503 -1.443674942
## 434 434 0 44.44442 12.58140 2.306337 0.356661385 0.193100685
## 435 435 0 58.00912 11.93226 3.704987 0.960284182 -4.913095040
## 436 436 0 25.23223 13.76184 4.237650 0.843008434 -0.024266489
## 437 437 0 39.35843 10.59202 6.314168 0.069633855 2.516814691
## 438 438 0 75.24296 11.57476 8.410532 0.705017806 0.084102223
## 439 439 0 27.71826 15.27168 3.156523 0.991856595 -2.493728337
## 440 440 0 77.22175 12.61479 4.801405 0.468704649 3.656407070
## 441 441 0 68.00547 11.32797 5.707440 0.232078453 1.071899179
## 442 442 0 21.69133 10.14345 2.903833 0.777419007 3.068916317
## 443 443 0 22.09856 15.06121 2.748912 0.974392610 1.869526910
## 444 444 0 17.28946 13.51993 6.485765 0.593751166 0.229774947
## 445 445 0 51.56032 15.28846 1.815659 0.698202156 3.864731822
## 446 446 0 30.56757 10.48010 2.671005 0.271645685 1.054050303
## 447 447 0 35.74800 12.86075 9.352652 0.065908138 -1.167452722
## 448 448 0 18.56012 12.25494 5.663800 0.804115437 -1.116673997
## 449 449 0 45.07920 13.63505 1.469759 0.149348758 -0.562335853
## 450 450 0 75.34443 13.05212 8.924711 0.118687865 -1.821327424
## 451 451 0 55.93422 13.19786 8.018309 0.619074552 -5.578428216
## 452 452 0 47.12225 15.37706 4.445255 0.567603333 -0.698005172
## 453 453 0 10.07339 12.83912 6.382477 0.068685685 -2.050503140
## 454 454 0 41.09557 10.66078 9.783400 0.571956698 1.645759030
## 455 455 0 52.91695 13.03602 9.642042 0.419087881 0.740359177
## 456 456 0 78.31311 15.40721 3.709094 0.570784008 1.465872538
## 457 457 0 52.62335 10.74554 9.189306 0.437095043 0.016387802
## 458 458 0 72.42658 10.88964 7.646019 0.117650913 -4.610150051
## 459 459 0 41.27513 12.68254 8.891114 0.552324052 1.796510054
## 460 460 0 28.93096 11.11435 9.001809 0.900962865 2.716604656
## 461 461 0 60.53190 15.99563 8.394791 0.902134400 1.363844593
## 462 462 0 56.59868 15.82920 6.477396 0.763885150 1.642970888
## 463 463 0 73.50876 14.23739 3.684920 0.688357751 0.454739817
## 464 464 0 49.12118 12.38653 2.011254 0.511876340 0.116387081
## 465 465 0 64.76135 12.00728 3.193714 0.582948487 1.834576541
## 466 466 0 24.86429 13.07956 7.080961 0.700579189 0.090016493
## 467 467 0 12.27289 13.91044 8.092113 0.599398965 -0.322413776
## 468 468 0 57.35645 12.55221 1.117343 0.412707972 2.263467593
## 469 469 0 24.39311 14.69806 3.962089 0.892409819 1.438353770
## 470 470 0 54.43531 11.41509 9.663549 0.186208201 -4.863209631
## 471 471 0 48.09537 13.77448 2.697798 0.820922712 0.434813743
## 472 472 0 12.01373 14.33048 5.441673 0.785917595 2.605085344
## 473 473 0 77.01277 15.76601 6.158280 0.753946979 -0.927764727
## 474 474 0 10.62894 10.39360 9.384675 0.846822963 -2.055509548
## 475 475 0 30.21185 15.23776 9.488815 0.352104198 0.535589579
## 476 476 0 47.09577 11.42589 3.994019 0.859347369 2.956419587
## 477 477 0 33.37782 14.86671 3.397280 0.415468908 2.150559478
## 478 478 0 54.76141 13.84148 6.660449 0.959526783 -0.505611292
## 479 479 0 38.48097 15.17031 5.560408 0.300289541 -0.486370795
## 480 480 0 21.71850 12.50159 9.884203 0.381214523 2.661085023
## 481 481 0 44.76446 10.80835 2.491507 0.189111282 -2.227285766
## 482 482 0 78.85632 12.94730 4.128994 0.450103302 1.358801349
## 483 483 0 12.45272 11.86493 9.149346 0.024618509 0.199235901
## 484 484 0 41.54095 14.20670 7.517626 0.168632520 2.440411224
## 485 485 0 72.02149 11.63221 4.584868 0.855832749 -2.413333458
## 486 486 0 73.99236 11.09845 8.177046 0.637962416 -1.625941057
## 487 487 0 32.00560 13.15439 4.936094 0.813396239 -3.914097369
## 488 488 0 47.53722 11.77040 1.492048 0.591462354 -0.985854395
## 489 489 0 13.67741 12.50723 5.370721 0.331698807 2.769196835
## 490 490 0 21.03165 13.24397 2.484302 0.534633218 1.097118106
## 491 491 0 24.88361 11.38887 7.692265 0.428352930 0.584143113
## 492 492 0 46.74800 10.39002 7.521643 0.492999859 0.601150877
## 493 493 0 74.06624 12.62446 4.453065 0.393895330 2.805989602
## 494 494 0 78.86219 13.02513 4.766772 0.566620105 -3.118752671
## 495 495 0 51.67231 12.00818 8.718667 0.820933729 3.933927062
## 496 496 0 75.47612 11.62463 8.586977 0.925791845 -2.065576918
## 497 497 0 16.01227 11.45565 1.636149 0.328830353 -1.045087670
## 498 498 0 26.61077 13.49038 9.418296 0.445244231 0.437028301
## 499 499 0 79.30805 14.24209 2.974569 0.640624065 -2.192106166
## 500 500 0 65.99257 14.01162 8.658432 0.650782300 -2.395892566
## 501 501 1 128.66180 10.72696 9.842567 0.733573247 1.958298245
## 502 502 1 118.93565 12.54715 5.410028 0.558840320 -1.176928284
## 503 503 1 81.17555 10.06840 7.058892 0.530795175 -3.090019697
## 504 504 1 116.49117 11.99777 8.312494 0.421241399 -1.043119003
## 505 505 1 120.40721 11.26685 8.789099 0.190276575 -1.097638284
## 506 506 1 124.44620 12.11541 2.690736 0.251705760 0.327654239
## 507 507 1 86.30819 15.33343 1.084810 0.779715861 2.012306613
## 508 508 1 62.86647 14.86820 3.493950 0.088785803 0.924235662
## 509 509 1 125.61412 15.91995 1.803818 0.965712849 -1.659520335
## 510 510 1 127.66988 13.28833 9.464334 0.536303572 0.436965973
## 511 511 1 100.48511 15.45639 8.177680 0.961915815 0.826346850
## 512 512 1 75.36811 14.30498 8.412155 0.356352651 -0.256439963
## 513 513 1 71.39705 15.57216 1.519986 0.148133726 -1.434952820
## 514 514 1 67.54737 11.50367 9.207564 0.004068035 0.446973439
## 515 515 1 71.24889 15.88482 6.028969 0.273149203 2.055073565
## 516 516 1 78.29066 10.17189 3.263527 0.990995826 1.394537006
## 517 517 1 91.07768 10.54245 9.475874 0.098906163 -2.428855047
## 518 518 1 62.55569 10.13990 5.413076 0.190727073 -0.288624848
## 519 519 1 60.77968 10.89944 6.961769 0.338054156 1.707642799
## 520 520 1 73.21243 13.12869 9.325264 0.525336310 0.970150572
## 521 521 1 88.71964 10.96239 9.995992 0.955344328 -0.866013689
## 522 522 1 81.73142 12.52408 1.479711 0.561156171 -5.029804220
## 523 523 1 108.55083 12.74002 4.029586 0.375264286 -0.378969505
## 524 524 1 99.13282 14.62927 7.985373 0.421398927 1.364618162
## 525 525 1 94.94423 12.15862 2.176556 0.835268881 0.854050986
## 526 526 1 91.60096 14.73898 5.382285 0.706959961 1.884640731
## 527 527 1 110.37984 15.13820 6.026520 0.931825949 -2.082300174
## 528 528 1 66.28789 13.32718 8.722159 0.905808832 -0.655171984
## 529 529 1 122.05559 13.63346 5.881148 0.632011099 1.569003840
## 530 530 1 101.88432 15.08065 8.859807 0.558488472 -2.211460514
## 531 531 1 107.63785 13.20073 3.538977 0.320380337 -3.627886013
## 532 532 1 82.61459 14.10887 1.868199 0.129742371 2.882490492
## 533 533 1 103.36896 14.16292 4.920868 0.688582694 0.840716809
## 534 534 1 70.77348 14.40748 1.300076 0.678891051 -1.180857252
## 535 535 1 68.18001 11.38390 9.189775 0.956523859 -0.551879558
## 536 536 1 81.24211 12.70323 8.040088 0.538861470 0.216789107
## 537 537 1 117.15666 12.06597 9.451935 0.565930062 2.985341377
## 538 538 1 84.67316 14.60338 6.103469 0.178594198 3.342425164
## 539 539 1 86.73614 14.22652 4.217756 0.783192700 0.218142948
## 540 540 1 82.91437 12.12173 6.775294 0.198808310 3.026433443
## 541 541 1 124.51124 13.77259 4.309386 0.667265926 -1.243277288
## 542 542 1 125.70890 13.99376 2.763948 0.187139824 1.120823373
## 543 543 1 88.47141 15.23287 3.828099 0.597400467 0.063777948
## 544 544 1 123.10259 14.68605 7.697304 0.279623081 -1.208862613
## 545 545 1 108.77238 12.96582 2.400486 0.377032092 -0.292298341
## 546 546 1 60.36301 11.14860 8.828921 0.872471569 -2.777232136
## 547 547 1 73.41887 13.19359 4.073165 0.387847248 -1.265981666
## 548 548 1 96.32505 14.56277 3.779774 0.633885217 2.868389223
## 549 549 1 80.48531 10.74353 3.192251 0.100182238 -4.038415103
## 550 550 1 116.28010 14.26585 3.141220 0.532891773 0.890445084
## 551 551 1 60.16560 13.57571 2.028837 0.355560557 -0.631199106
## 552 552 1 99.53252 10.06401 9.923850 0.464448719 0.755717967
## 553 553 1 63.28620 13.22484 2.183159 0.307152933 3.447417305
## 554 554 1 75.30975 15.12309 5.996634 0.216659255 2.516900424
## 555 555 1 116.16915 10.77872 1.161179 0.130715740 -2.564956169
## 556 556 1 88.63016 10.92521 7.618076 0.491400612 -0.152639219
## 557 557 1 70.08382 13.43456 7.519779 0.740693916 -3.628030131
## 558 558 1 61.41746 10.91389 6.844805 0.721925867 0.885973240
## 559 559 1 109.50240 10.96977 7.644455 0.057342862 0.469475304
## 560 560 1 68.38059 10.33977 2.077131 0.699653230 1.279405953
## 561 561 1 111.00728 10.36981 6.218477 0.809031210 0.645315698
## 562 562 1 104.42993 15.57706 1.273702 0.070940701 -2.895014077
## 563 563 1 108.73660 14.86551 7.662295 0.691943090 0.240150656
## 564 564 1 91.50070 10.08357 2.333113 0.856674199 -0.063268636
## 565 565 1 110.60263 12.07608 5.739710 0.787290401 5.035617933
## 566 566 1 71.52434 13.01305 4.668341 0.511854753 0.212648481
## 567 567 1 84.76217 10.05980 2.257730 0.919901961 -2.963364288
## 568 568 1 72.82258 12.34789 5.009760 0.566551746 2.496867696
## 569 569 1 85.79820 10.79575 2.863581 0.746567932 -1.950036910
## 570 570 1 88.19628 10.99241 9.516537 0.801336104 -2.764405890
## 571 571 1 96.64884 11.95994 9.729980 0.478648720 1.359728280
## 572 572 1 72.98790 10.16519 3.360097 0.369962405 0.740085020
## 573 573 1 86.87392 11.56993 1.064414 0.725716817 0.806357599
## 574 574 1 72.69397 10.13630 4.276559 0.183189944 2.742726491
## 575 575 1 128.66095 11.95749 3.366398 0.042136591 -3.167278778
## 576 576 1 69.49875 10.86528 6.310217 0.269993082 -1.002418940
## 577 577 1 111.60246 14.39537 2.529886 0.009589370 0.650333932
## 578 578 1 84.29782 13.09225 4.739717 0.850706898 2.397808026
## 579 579 1 103.99697 11.47010 5.840125 0.574324733 -1.359766516
## 580 580 1 100.14833 11.07764 8.859306 0.317493263 0.240592984
## 581 581 1 86.82977 13.17446 8.267386 0.613536613 3.457011322
## 582 582 1 83.80937 12.09852 8.289586 0.026975339 1.994759478
## 583 583 1 107.42773 15.14236 1.183422 0.465367281 -2.718692078
## 584 584 1 105.23397 15.29779 7.669630 0.308770873 0.991494857
## 585 585 1 124.66997 14.28340 7.613566 0.115860842 -3.110150036
## 586 586 1 70.51214 13.22146 4.183743 0.687451377 0.734998131
## 587 587 1 125.60664 13.96650 3.786244 0.920541531 -0.343766905
## 588 588 1 67.00069 10.23857 4.556896 0.385836244 1.890027910
## 589 589 1 129.13688 12.73888 6.067275 0.712776668 -4.194843772
## 590 590 1 114.81607 13.55735 8.181829 0.849765031 -0.005307291
## 591 591 1 100.10045 14.41665 6.455192 0.900119539 -3.740992238
## 592 592 1 102.66591 11.63706 1.274246 0.029162220 -2.898881462
## 593 593 1 122.99356 12.13196 1.101764 0.727489650 -1.993138780
## 594 594 1 77.21096 10.52368 5.085496 0.242091433 4.764579017
## 595 595 1 101.72846 11.44871 9.913190 0.478179386 3.529547502
## 596 596 1 101.61945 10.91539 3.368673 0.520216604 2.854333047
## 597 597 1 64.85063 10.07019 5.270962 0.105249825 0.670770606
## 598 598 1 122.76171 12.04010 4.640172 0.424886371 -2.561575948
## 599 599 1 105.66687 15.14478 5.674720 0.247573998 -2.417037822
## 600 600 1 121.55837 15.76453 3.838335 0.876601125 4.319802429
## 601 601 1 112.94723 11.26197 9.339986 0.335283186 1.143127941
## 602 602 1 108.78830 15.95872 8.944861 0.817788030 -1.433041168
## 603 603 1 116.37886 15.35213 1.661092 0.534897401 -1.763805281
## 604 604 1 68.11584 13.22075 1.509737 0.370609576 -1.987583699
## 605 605 1 115.81458 14.96221 3.205955 0.853914504 0.782482970
## 606 606 1 108.80276 12.61829 3.534472 0.584453374 -2.079368269
## 607 607 1 124.31232 14.09674 5.495373 0.874131650 1.242205911
## 608 608 1 100.47890 11.85367 3.709567 0.848970144 -0.785055016
## 609 609 1 84.79292 12.66472 4.245025 0.210742827 -2.371520048
## 610 610 1 94.80674 14.12869 4.682103 0.196270232 -1.254908821
## 611 611 1 119.10902 12.35150 6.882350 0.076619409 -5.312176280
## 612 612 1 128.39880 12.11254 8.287847 0.388382067 1.495863491
## 613 613 1 91.75451 14.22582 2.428875 0.046452277 -0.712180103
## 614 614 1 128.10039 10.08225 5.597498 0.536057666 0.742354880
## 615 615 1 79.93781 12.85491 4.187477 0.919255650 -0.690143010
## 616 616 1 89.67583 15.15384 9.199450 0.366083281 -2.179853178
## 617 617 1 66.98902 13.83889 5.760551 0.727089552 -1.783532199
## 618 618 1 96.27759 13.97159 7.148535 0.572790738 0.470385544
## 619 619 1 99.27359 10.84785 5.337492 0.219980547 -3.813725218
## 620 620 1 83.31696 11.34227 9.585524 0.016572248 0.329368037
## 621 621 1 100.70485 13.53785 9.016187 0.578994814 -1.905807995
## 622 622 1 79.63926 14.54802 7.342615 0.012052615 -1.445019587
## 623 623 1 60.00277 14.87725 4.646124 0.672086125 -0.124133664
## 624 624 1 117.00113 15.51806 6.880422 0.425578709 -3.119592867
## 625 625 1 105.69794 15.33323 2.506968 0.344894752 0.018806660
## 626 626 1 67.73854 12.43904 2.800202 0.841028990 -0.076868162
## 627 627 1 86.29111 14.23502 9.810102 0.133001855 -1.337569948
## 628 628 1 76.85333 13.47702 2.225704 0.551047304 1.648833208
## 629 629 1 117.46922 13.51376 3.711961 0.232871626 -0.495534112
## 630 630 1 68.86402 11.23073 4.914586 0.940665438 -1.364409813
## 631 631 1 102.49750 10.39358 6.563876 0.464597968 0.912590618
## 632 632 1 120.54398 11.80226 6.003960 0.714310799 -0.500188497
## 633 633 1 125.11897 14.30381 7.497211 0.444596667 0.212362509
## 634 634 1 124.37002 12.92563 2.247579 0.702001183 0.089519874
## 635 635 1 113.44261 11.01468 6.888443 0.660722377 3.204415977
## 636 636 1 91.35938 10.29751 4.031388 0.052484121 2.321986302
## 637 637 1 100.94469 13.81946 3.876487 0.242204686 1.786820992
## 638 638 1 88.44689 11.82081 7.721175 0.875468428 -3.597235446
## 639 639 1 73.60690 14.12891 2.934396 0.834615117 3.949500448
## 640 640 1 68.98993 13.17763 3.801556 0.942990531 -1.055318197
## 641 641 1 71.37233 12.82062 6.614387 0.501353964 -1.493319310
## 642 642 1 97.75019 12.51039 3.995718 0.523871491 1.301660023
## 643 643 1 122.41532 15.43364 6.622390 0.618626134 -0.040323685
## 644 644 1 70.93849 15.81032 1.419149 0.276575797 -0.522207233
## 645 645 1 87.83394 14.98761 5.109594 0.502326638 -1.024051614
## 646 646 1 95.53466 14.44939 9.959573 0.729360538 0.252474281
## 647 647 1 114.92468 15.87622 6.743346 0.909974701 -0.227032148
## 648 648 1 120.51747 15.05331 9.510691 0.764865327 -0.117811617
## 649 649 1 67.05864 12.96700 7.712338 0.367396888 3.199803997
## 650 650 1 64.30626 13.32602 2.196035 0.874782466 0.430597766
## 651 651 1 78.56548 14.63165 1.933291 0.363951449 0.645390277
## 652 652 1 95.52571 13.99748 6.812210 0.290355034 2.444122091
## 653 653 1 107.18505 14.94035 2.026314 0.320897220 0.031706245
## 654 654 1 119.37508 15.35792 3.900137 0.680569881 -3.058047611
## 655 655 1 80.52082 13.91578 2.467172 0.650990049 -0.464629300
## 656 656 1 88.85331 14.99600 2.439910 0.471730644 1.799926499
## 657 657 1 94.61190 15.69955 2.133365 0.831765355 -2.773268668
## 658 658 1 106.67111 14.78894 6.916448 0.970336368 -0.153340925
## 659 659 1 120.04675 13.66810 1.025630 0.789545402 -0.063172595
## 660 660 1 82.29287 11.90016 2.363340 0.534084493 2.094907938
## 661 661 1 124.70957 14.92101 6.247593 0.810891195 0.719090229
## 662 662 1 125.22779 15.59045 2.555901 0.992043210 3.609473695
## 663 663 1 122.86684 13.47476 2.937177 0.006240772 -1.649145972
## 664 664 1 107.67335 11.36824 3.631177 0.983962921 1.117340726
## 665 665 1 66.40335 13.98975 5.651022 0.833072336 1.539870690
## 666 666 1 83.17587 12.21274 3.810252 0.559758361 -1.309890835
## 667 667 1 112.32418 11.53442 6.897642 0.855965885 0.455295365
## 668 668 1 97.59599 10.98855 7.152317 0.877397053 0.982601655
## 669 669 1 113.72329 15.75511 8.068329 0.913725962 0.574179553
## 670 670 1 83.57573 15.13423 6.396247 0.417780723 -2.924459911
## 671 671 1 102.18222 13.04768 7.747705 0.048217680 3.427025008
## 672 672 1 124.83629 15.62546 1.714748 0.394369852 -2.246730066
## 673 673 1 106.81785 10.38022 1.962464 0.526423587 3.755968618
## 674 674 1 111.71839 11.32421 7.426853 0.768984383 -1.332684511
## 675 675 1 79.97339 10.72129 4.072383 0.886890683 3.186964185
## 676 676 1 65.38329 10.43893 5.413427 0.596512839 -3.001085667
## 677 677 1 98.55359 13.81223 8.275291 0.964907162 -2.755431076
## 678 678 1 90.04046 11.76640 3.456765 0.190046407 0.796872471
## 679 679 1 76.78105 14.02580 6.090795 0.021604648 -0.359324758
## 680 680 1 96.73795 11.07538 7.442501 0.220073558 0.392551750
## 681 681 1 62.91359 10.93923 2.413478 0.952720864 -1.969367397
## 682 682 1 80.64682 10.72109 3.925102 0.075342448 -0.664207236
## 683 683 1 70.74408 14.09089 7.029395 0.372088801 0.976304301
## 684 684 1 124.65688 10.13219 9.359171 0.846338860 0.321682448
## 685 685 1 65.63758 15.61733 1.900761 0.630872838 -2.430095385
## 686 686 1 129.53668 11.23610 7.916057 0.786878324 -0.930372039
## 687 687 1 60.86914 10.79154 5.259413 0.897190825 -2.073781573
## 688 688 1 72.65489 15.69691 3.645109 0.181268512 1.494743796
## 689 689 1 125.84247 13.61361 8.676099 0.449239363 1.434543581
## 690 690 1 72.61221 14.86969 8.070578 0.438139186 0.094248311
## 691 691 1 111.90388 11.54071 5.020170 0.489539095 -4.324966063
## 692 692 1 94.17229 10.23505 8.133582 0.135543143 -2.132981754
## 693 693 1 87.11912 13.53680 8.867806 0.889156068 -2.128366891
## 694 694 1 60.49925 11.74020 1.162716 0.409748563 -0.894567881
## 695 695 1 109.08996 12.09353 3.285278 0.064680084 -0.463733146
## 696 696 1 116.03308 13.95364 3.081476 0.700857568 0.946343576
## 697 697 1 69.99515 13.53543 7.706756 0.190040248 -1.251637646
## 698 698 1 120.86060 15.01059 3.227621 0.986207147 -2.186969202
## 699 699 1 91.74006 14.81395 9.193238 0.788563289 -0.755242928
## 700 700 1 97.76639 12.54797 5.700118 0.404303331 0.055526762
## 701 701 1 75.84982 14.85137 2.248547 0.577132475 -2.499587244
## 702 702 1 93.59963 13.98422 6.451097 0.620164218 -2.934682712
## 703 703 1 66.76562 15.53498 1.555949 0.170714606 2.493795487
## 704 704 1 77.26716 13.53868 5.305663 0.236936145 -0.612275691
## 705 705 1 128.68622 13.77983 5.789284 0.943035304 -1.312156147
## 706 706 1 73.61578 12.62189 3.768309 0.537431362 1.465631383
## 707 707 1 124.18422 13.39120 1.464339 0.796731358 0.734408736
## 708 708 1 113.16186 13.03548 3.583279 0.350104789 1.618084239
## 709 709 1 60.89483 13.31298 3.457367 0.819466512 -0.934459593
## 710 710 1 102.88727 15.19005 7.894246 0.506226445 -3.142365978
## 711 711 1 90.44230 15.42025 3.606316 0.757747906 -1.063678666
## 712 712 1 100.15040 14.26107 5.592955 0.958778950 -2.024617171
## 713 713 1 100.45306 14.14267 7.887285 0.967471450 -1.160155698
## 714 714 1 115.42234 13.73483 5.694462 0.274761826 -2.277526094
## 715 715 1 99.68531 11.23610 5.120868 0.141498126 1.845598973
## 716 716 1 61.87310 15.49049 9.360025 0.880168887 2.687201553
## 717 717 1 92.21379 13.32397 3.456941 0.943498643 -1.791930129
## 718 718 1 113.08168 10.99205 2.796868 0.575637904 -2.719057013
## 719 719 1 93.80151 10.31319 3.970715 0.068930513 1.761884016
## 720 720 1 119.33399 11.59464 1.514538 0.860082512 -0.822072501
## 721 721 1 120.66363 15.46509 6.436386 0.247315433 -3.392295821
## 722 722 1 68.18178 15.83698 3.948586 0.946226032 1.804828586
## 723 723 1 86.42346 12.89580 8.006320 0.698543977 2.774106431
## 724 724 1 117.25587 10.68027 7.536443 0.786728258 0.236009351
## 725 725 1 113.12018 15.79698 4.447335 0.648623538 -0.824536988
## 726 726 1 118.84996 14.51341 3.870766 0.583774102 -1.925611042
## 727 727 1 97.41712 14.99895 6.181041 0.049262422 -2.933390453
## 728 728 1 126.59693 12.10229 6.685551 0.605355898 -2.014270044
## 729 729 1 92.56068 12.95225 3.316393 0.600832550 1.975496695
## 730 730 1 114.16979 13.95435 5.310274 0.669457132 0.245743356
## 731 731 1 74.23831 12.99144 1.209058 0.926584445 0.886005981
## 732 732 1 64.80089 11.26891 8.339061 0.083895234 -1.498962621
## 733 733 1 76.01434 14.08214 8.414146 0.527010944 1.349385714
## 734 734 1 64.60689 11.02725 5.049899 0.337871642 -2.671991386
## 735 735 1 69.80955 11.34497 2.834543 0.276031733 -2.815077174
## 736 736 1 95.82437 10.46171 5.364932 0.145861991 2.930365834
## 737 737 1 64.51909 13.54745 6.127444 0.631609143 -3.249308875
## 738 738 1 96.76814 11.44662 3.746455 0.288773036 -0.759417042
## 739 739 1 125.12454 13.73646 9.941703 0.678399548 -2.998015444
## 740 740 1 111.98382 10.93114 2.317100 0.461637762 0.022783148
## 741 741 1 110.43015 12.19728 2.277675 0.420070658 2.070793728
## 742 742 1 81.54323 14.78346 5.865412 0.858067909 -1.926970153
## 743 743 1 93.34460 15.32483 6.655722 0.216228077 -1.381423409
## 744 744 1 117.80161 15.49349 8.145523 0.745576130 1.313749812
## 745 745 1 118.43294 13.89803 1.399790 0.760412545 -0.714996649
## 746 746 1 76.26346 13.45661 2.279751 0.521217529 0.730690652
## 747 747 1 99.85276 15.16965 1.372274 0.599436574 -3.835138558
## 748 748 1 107.93320 10.59285 1.671725 0.784783754 0.691425541
## 749 749 1 77.29535 12.22027 7.205434 0.296947941 -1.647112498
## 750 750 1 83.80133 13.93298 5.434671 0.165262563 0.581366048
## 751 751 1 90.35914 15.45105 9.617765 0.739081182 -0.712120503
## 752 752 1 90.54078 12.89464 8.898616 0.339617966 0.653473519
## 753 753 1 127.18688 15.45633 1.810817 0.380740592 1.845939418
## 754 754 1 129.81736 13.97740 9.107462 0.533824399 0.301885324
## 755 755 1 62.28284 11.71465 5.784655 0.126382711 0.095108339
## 756 756 1 102.91196 12.34072 5.523952 0.689560780 -2.762573030
## 757 757 1 112.00049 13.87945 8.419225 0.870230646 0.926028441
## 758 758 1 65.63966 12.78283 3.451166 0.085905329 1.222927790
## 759 759 1 67.95763 10.86973 9.434878 0.018813415 -0.707746807
## 760 760 1 92.24004 15.56455 9.386492 0.383654911 -2.540284348
## 761 761 1 70.07838 10.75345 8.984368 0.979450461 -2.065785020
## 762 762 1 99.18538 15.87145 8.509946 0.265763845 -0.247612237
## 763 763 1 78.17739 11.60416 8.820454 0.261391284 -1.285820382
## 764 764 1 115.12666 12.30540 1.491357 0.147621043 -4.784117981
## 765 765 1 116.54013 14.28847 5.916094 0.879986943 -0.961035995
## 766 766 1 101.16522 13.16351 7.000342 0.757895573 -1.914839942
## 767 767 1 128.71937 10.81737 1.321057 0.007376764 3.481907165
## 768 768 1 118.72916 10.33225 4.628460 0.946930036 -0.999955675
## 769 769 1 79.04001 12.36624 5.190010 0.921786223 -0.844231863
## 770 770 1 119.75313 14.89535 3.722332 0.745224422 3.232587937
## 771 771 1 73.11096 10.43979 7.294592 0.927307247 1.562407100
## 772 772 1 121.52245 12.31770 8.904658 0.223819796 -1.861876999
## 773 773 1 116.42890 14.21476 3.856192 0.646500705 3.628689023
## 774 774 1 67.67417 14.51048 3.260990 0.955877439 2.151393541
## 775 775 1 123.90623 10.80742 6.728148 0.223675688 0.934398843
## 776 776 1 114.18753 15.58507 1.888599 0.530400806 -3.298535360
## 777 777 1 80.03984 14.31675 5.153271 0.374249028 0.353023278
## 778 778 1 100.82998 14.15958 7.227927 0.379095614 -2.752136463
## 779 779 1 89.89011 15.95738 1.007749 0.775276299 1.669273503
## 780 780 1 106.94156 11.75202 4.708048 0.178713327 -3.274778552
## 781 781 1 84.48934 10.22288 2.868033 0.214547804 0.764700496
## 782 782 1 72.41813 10.86631 7.919526 0.033449943 4.408555059
## 783 783 1 99.82228 15.58456 7.305010 0.074730873 4.284372083
## 784 784 1 113.43736 11.07421 5.784042 0.728657798 -2.079603634
## 785 785 1 64.69823 12.65759 2.467650 0.305028839 -1.421859500
## 786 786 1 75.46050 11.25597 7.973237 0.343189279 0.024790398
## 787 787 1 114.91221 13.21048 5.100130 0.528802793 -0.931324488
## 788 788 1 117.46461 15.22909 1.404643 0.821001653 -1.796003839
## 789 789 1 90.01676 10.03857 2.064083 0.380905771 0.431652400
## 790 790 1 126.28512 14.40055 8.244711 0.091260119 -0.981719332
## 791 791 1 84.92561 13.24895 9.545487 0.484181121 0.789956072
## 792 792 1 90.50529 13.29449 7.044221 0.888143817 1.156264785
## 793 793 1 74.94761 11.00718 6.996510 0.183917166 0.753865074
## 794 794 1 89.44987 10.11819 3.789966 0.900759106 0.969073834
## 795 795 1 117.51907 15.77435 4.575295 0.710756763 -1.166985842
## 796 796 1 119.35231 12.79235 5.653651 0.197735796 4.001080483
## 797 797 1 101.51062 13.67367 4.370296 0.307259406 -1.152217749
## 798 798 1 71.18890 15.97968 2.340614 0.934100420 0.636037469
## 799 799 1 117.20777 13.56837 4.345823 0.334281497 0.762162670
## 800 800 1 111.79070 14.35494 5.867418 0.094079197 -0.540540765
## 801 801 1 90.19829 13.47963 9.128835 0.199261877 0.854404420
## 802 802 1 63.76208 13.10670 1.566459 0.361100778 -0.341188404
## 803 803 1 87.87879 10.34009 1.751926 0.165347406 -0.704232592
## 804 804 1 92.74724 13.04732 1.489515 0.790722335 -0.292638369
## 805 805 1 125.37204 14.28691 1.883514 0.076147071 -2.415630757
## 806 806 1 95.70414 10.66772 8.836140 0.833280254 0.255755990
## 807 807 1 94.83547 10.99651 8.237204 0.903599565 0.206725805
## 808 808 1 111.26485 12.74728 9.515839 0.896159229 0.383055880
## 809 809 1 119.38825 14.34951 4.577364 0.099946887 -4.064852612
## 810 810 1 97.52845 12.98478 1.039920 0.765594074 -4.965654881
## 811 811 1 96.37634 11.18740 5.610330 0.613600101 -0.672887205
## 812 812 1 121.45111 14.59983 8.571083 0.034323357 0.142411124
## 813 813 1 74.01026 12.91856 5.463008 0.277183793 0.193103394
## 814 814 1 90.16813 14.86607 8.784449 0.266558505 -2.102536820
## 815 815 1 98.78566 12.87281 1.480893 0.304596241 -1.151559239
## 816 816 1 109.64603 15.39135 7.480122 0.603493642 -3.053381519
## 817 817 1 68.06376 15.75714 9.759064 0.120329102 -0.406477724
## 818 818 1 99.39315 10.22062 6.359835 0.034739005 -1.161136142
## 819 819 1 109.53204 13.36598 9.904824 0.808067198 -0.254125421
## 820 820 1 61.60051 12.40140 3.414683 0.704241985 -5.201512755
## 821 821 1 126.19986 10.55646 9.597852 0.149063971 -0.166835304
## 822 822 1 121.23712 14.32219 8.657806 0.382685058 -0.771510011
## 823 823 1 73.29254 15.69355 8.914273 0.115114406 1.134344264
## 824 824 1 93.04846 10.56928 7.638010 0.364100066 -3.505517076
## 825 825 1 68.40508 14.37989 9.323273 0.625478977 0.021003991
## 826 826 1 109.01540 13.96434 8.093268 0.802281764 1.749272367
## 827 827 1 91.74212 15.37827 1.678453 0.627345562 -1.347390423
## 828 828 1 128.45766 11.39661 6.191793 0.858417803 -4.574479374
## 829 829 1 81.03610 12.99268 2.170442 0.737306650 1.103839993
## 830 830 1 77.67747 14.60642 3.459082 0.084442680 0.146617812
## 831 831 1 82.53797 11.00755 4.496456 0.088625142 2.512056475
## 832 832 1 115.79180 14.43925 8.119670 0.333157307 0.344339410
## 833 833 1 101.27481 10.26034 2.641293 0.448123192 1.707180117
## 834 834 1 65.18917 10.60880 6.505170 0.144052125 -2.348311184
## 835 835 1 65.12984 11.99591 6.704008 0.767968429 -1.448789447
## 836 836 1 87.35301 10.42211 1.171016 0.258675485 -0.034677057
## 837 837 1 98.14375 14.52648 5.294619 0.632369466 -2.071737325
## 838 838 1 76.57848 10.32408 4.950282 0.511755201 -0.214540182
## 839 839 1 71.41934 11.37178 4.276880 0.731258655 -4.726200367
## 840 840 1 92.71166 11.40524 6.706767 0.624363769 4.348925192
## 841 841 1 89.16617 15.41894 2.473601 0.454263484 1.360967536
## 842 842 1 78.77430 10.68532 1.678620 0.751182706 -0.516422160
## 843 843 1 86.54380 12.90789 3.774293 0.204043892 1.070929665
## 844 844 1 112.22534 10.98999 6.261843 0.465179404 -0.544372591
## 845 845 1 114.24759 14.55753 9.855137 0.744593292 -3.309382084
## 846 846 1 107.24334 14.76041 3.406785 0.223212030 -0.029637332
## 847 847 1 67.47713 14.16465 5.287874 0.133215721 -0.400701112
## 848 848 1 79.20286 12.40423 8.253723 0.640957363 -1.472053541
## 849 849 1 91.48384 15.35620 1.430788 0.740589264 0.159789538
## 850 850 1 105.07031 12.39970 6.104247 0.217714895 0.748622401
## 851 851 1 96.99809 12.46681 6.705758 0.143792724 -3.184569640
## 852 852 1 74.55964 13.91507 2.702395 0.709151715 -3.081350464
## 853 853 1 94.36184 15.17391 2.468331 0.416583213 -0.896775984
## 854 854 1 93.95225 10.72583 1.501133 0.615675966 3.019130459
## 855 855 1 92.55526 13.75733 5.725047 0.208611771 -1.430971348
## 856 856 1 121.87679 12.28687 8.347025 0.910764635 1.127686464
## 857 857 1 119.16454 13.61097 2.264540 0.088515131 1.001427451
## 858 858 1 65.48211 15.39274 9.820744 0.104241883 0.237653100
## 859 859 1 123.13018 15.45984 3.483754 0.378566603 -0.421331238
## 860 860 1 112.94588 10.39896 8.492345 0.295793874 -1.729449820
## 861 861 1 99.79611 11.85426 2.751139 0.560907013 -0.934284470
## 862 862 1 128.81218 12.05116 1.294432 0.647632089 0.578774768
## 863 863 1 102.53941 15.63125 4.045210 0.585214156 -2.472602550
## 864 864 1 74.32467 11.12584 7.873902 0.293241639 -2.689835794
## 865 865 1 85.61050 12.72429 2.235214 0.262277252 -2.535616946
## 866 866 1 74.25184 15.77992 8.642372 0.676780788 1.470308347
## 867 867 1 61.16482 10.20879 4.207782 0.672808917 3.120922936
## 868 868 1 101.62661 14.16146 8.437116 0.605661437 1.423287251
## 869 869 1 117.92963 13.67679 5.082756 0.949521262 0.269971670
## 870 870 1 119.96284 15.21376 8.512934 0.463967651 -1.640499234
## 871 871 1 104.54214 13.79753 3.503403 0.781583922 -0.210387683
## 872 872 1 101.12190 13.71672 3.055512 0.680438018 2.316706730
## 873 873 1 121.67386 11.70690 6.745709 0.925691732 0.375086776
## 874 874 1 78.09958 15.94691 6.174866 0.125229423 -2.821487592
## 875 875 1 122.62052 14.91876 5.320221 0.541878721 -1.377619686
## 876 876 1 71.28362 15.09083 6.560714 0.423920387 -2.043265481
## 877 877 1 84.01508 11.21675 1.672829 0.622960636 1.461679562
## 878 878 1 83.83640 14.94265 7.599268 0.665447699 1.403103073
## 879 879 1 95.07062 13.86073 8.711093 0.526958557 -3.125422698
## 880 880 1 74.75525 12.98821 6.174287 0.878476901 1.147747714
## 881 881 1 77.21824 11.39968 3.280870 0.203675221 0.588050715
## 882 882 1 66.47000 13.47943 3.177382 0.404835815 2.175125199
## 883 883 1 92.19110 12.78977 2.949719 0.057408864 -1.675002772
## 884 884 1 96.65097 15.62883 5.286923 0.920611986 0.673858696
## 885 885 1 70.29789 11.22277 2.803686 0.395449435 -0.439927631
## 886 886 1 84.78877 15.17089 7.752864 0.654078089 3.915035618
## 887 887 1 120.07888 10.74301 5.257067 0.005722257 -1.067701561
## 888 888 1 118.58783 10.77244 5.289815 0.780552653 0.793250328
## 889 889 1 63.40451 14.21686 1.701985 0.431208034 -2.205932997
## 890 890 1 82.41529 12.63001 7.766875 0.992183518 1.511988130
## 891 891 1 104.29864 11.06799 9.910165 0.010758920 -1.296039206
## 892 892 1 69.72484 15.02634 9.403935 0.141744281 -0.257333347
## 893 893 1 71.53668 12.22239 9.294540 0.157567139 -3.693204494
## 894 894 1 107.24620 10.28885 7.401250 0.039415686 -4.700594881
## 895 895 1 120.34082 10.68642 2.544550 0.427128974 -2.060501769
## 896 896 1 73.53097 15.13595 7.237829 0.998152871 -4.288105663
## 897 897 1 65.41864 15.44727 1.719038 0.126029180 0.362953544
## 898 898 1 104.28854 13.29002 5.797906 0.287970854 5.756501934
## 899 899 1 90.21635 13.54459 6.015179 0.053334902 -1.694156487
## 900 900 1 100.83311 15.24228 5.449754 0.666488632 -2.223110110
## 901 901 1 114.41333 10.69565 1.732085 0.415926708 -2.266569900
## 902 902 1 111.46711 14.17553 9.513986 0.526330660 1.161932739
## 903 903 1 98.81215 13.18665 1.494027 0.076828237 -2.346372999
## 904 904 1 64.03158 12.29729 8.623670 0.102929856 1.589964820
## 905 905 1 86.99765 13.73239 1.757368 0.878986786 1.221692171
## 906 906 1 121.38694 13.83314 8.394354 0.383608091 1.568780165
## 907 907 1 91.27185 13.46409 8.763861 0.767016722 1.786692263
## 908 908 1 113.17632 11.88341 1.287098 0.218049144 -0.990599133
## 909 909 1 88.93991 10.84951 1.029684 0.642272612 -4.110581539
## 910 910 1 110.67754 12.81983 1.265764 0.268889623 0.086169798
## 911 911 1 70.11585 15.43343 2.216005 0.333870495 3.518023997
## 912 912 1 116.44888 13.08352 5.204555 0.250105321 -0.881242793
## 913 913 1 110.04359 10.07145 8.329173 0.120456074 1.251462293
## 914 914 1 80.96256 12.51769 9.326745 0.607120472 -3.869876781
## 915 915 1 63.21167 10.47517 6.008244 0.522385150 -2.209223085
## 916 916 1 122.56117 11.29591 7.780740 0.813681706 -1.849116334
## 917 917 1 129.87233 11.95807 6.005015 0.609153562 -1.430360145
## 918 918 1 93.75220 11.11547 1.074807 0.226861587 -0.193399202
## 919 919 1 70.88462 11.63757 6.023085 0.677396464 0.431072655
## 920 920 1 83.87471 11.93908 8.325315 0.185537605 -1.215507279
## 921 921 1 110.97024 11.13914 3.658291 0.110714613 1.409657751
## 922 922 1 129.71463 12.73283 9.727714 0.336949135 -0.580232927
## 923 923 1 83.03318 10.02726 6.955190 0.950538547 0.074888340
## 924 924 1 123.80664 10.42603 9.424200 0.105615841 0.457216781
## 925 925 1 77.89265 11.74614 6.069410 0.252598227 4.147622427
## 926 926 1 115.28366 15.39517 2.033917 0.257623724 0.045996273
## 927 927 1 76.38479 15.39390 5.012366 0.945176459 -2.127657940
## 928 928 1 80.55940 10.09145 2.013794 0.001914541 0.960030977
## 929 929 1 108.91811 11.64846 3.426814 0.317932076 0.340027280
## 930 930 1 98.50044 15.49657 4.267978 0.716065221 1.408303306
## 931 931 1 78.91219 15.55249 9.946626 0.868492966 0.424315288
## 932 932 1 120.66532 11.07238 8.878380 0.035590990 3.512141793
## 933 933 1 73.75692 13.56749 9.265682 0.440328413 -2.459159483
## 934 934 1 68.80176 11.76999 5.851564 0.056297863 -2.103246120
## 935 935 1 129.42510 15.30974 2.751297 0.292849531 -1.036463181
## 936 936 1 92.67379 15.65476 1.780371 0.461245523 0.283456529
## 937 937 1 95.67407 12.15663 3.617341 0.796629138 0.826859049
## 938 938 1 79.14280 12.77758 9.890854 0.485043163 -0.370212212
## 939 939 1 67.65379 12.12713 7.286760 0.832663578 -1.530505460
## 940 940 1 72.06208 11.33001 5.753785 0.511623349 4.272432473
## 941 941 1 74.53368 14.49385 2.143333 0.356089468 0.442784106
## 942 942 1 91.36585 11.69451 9.376978 0.687910163 3.933435294
## 943 943 1 120.21630 11.75846 3.002397 0.638017626 0.255269465
## 944 944 1 98.75673 11.02294 8.725410 0.372632533 -1.334693660
## 945 945 1 94.39775 10.35349 9.216918 0.301751507 3.383828247
## 946 946 1 80.05900 15.90847 5.332174 0.226386187 -0.325884975
## 947 947 1 72.50384 14.11759 2.582663 0.333709213 4.535242607
## 948 948 1 75.37519 13.71110 6.505098 0.663000267 3.123393576
## 949 949 1 65.13319 14.27275 6.727987 0.900412282 2.482000795
## 950 950 1 84.59058 15.91783 3.807610 0.518788734 -2.084669103
## 951 951 1 74.38828 14.43660 4.407224 0.877551880 -2.244348393
## 952 952 1 75.93456 14.64013 3.075730 0.671435782 0.006621030
## 953 953 1 127.28339 12.47715 4.169853 0.544177347 2.757989920
## 954 954 1 128.92154 11.68123 6.772124 0.216609929 -1.903952635
## 955 955 1 83.94540 13.70128 8.700648 0.595246030 -0.955095474
## 956 956 1 126.34935 11.03850 5.309696 0.978473313 3.338406516
## 957 957 1 70.63722 13.65395 6.627876 0.821529897 -3.860889441
## 958 958 1 88.97862 10.40602 4.147083 0.144622922 -0.350320106
## 959 959 1 104.49527 12.14331 9.782972 0.908846331 0.160956083
## 960 960 1 76.57934 11.75208 3.891431 0.112736960 3.155822815
## 961 961 1 72.11622 13.57673 3.898254 0.021588273 -1.499158511
## 962 962 1 74.26400 14.42352 7.471447 0.250686914 1.243451628
## 963 963 1 83.64364 14.47746 1.955308 0.763441024 -1.719764456
## 964 964 1 109.41718 14.00595 4.408295 0.687606095 0.493106816
## 965 965 1 65.12206 14.91102 9.111260 0.301607602 0.740774652
## 966 966 1 61.43753 15.49483 6.933485 0.374322119 2.811566835
## 967 967 1 93.03626 15.13573 3.043136 0.666912356 -0.594958824
## 968 968 1 123.13960 10.87152 1.697125 0.007377125 2.643058468
## 969 969 1 70.98749 12.88016 6.749655 0.572886677 -1.947866004
## 970 970 1 106.82765 13.60476 6.862334 0.593117550 -1.213043871
## 971 971 1 118.50941 15.58879 5.620605 0.741224982 -1.950799148
## 972 972 1 76.34706 10.10801 5.909858 0.703599191 0.272607959
## 973 973 1 86.41824 12.59145 2.825040 0.579643369 -0.945040998
## 974 974 1 118.41939 10.96633 7.405993 0.451689861 -0.939625230
## 975 975 1 97.90634 11.10660 7.834082 0.450998180 0.265335413
## 976 976 1 101.44528 12.54459 3.196640 0.184395137 -0.688734463
## 977 977 1 72.42409 10.18375 7.208135 0.778163290 0.268289023
## 978 978 1 70.34485 14.40771 8.585012 0.707927299 2.363364451
## 979 979 1 126.42486 15.05019 4.644646 0.690364105 3.019951129
## 980 980 1 121.98236 14.91701 5.406012 0.564030894 2.530836654
## 981 981 1 93.09335 12.45262 1.344221 0.493018524 -1.010269966
## 982 982 1 128.94232 14.17554 8.386386 0.213137395 -3.414064224
## 983 983 1 80.97413 12.88060 7.835285 0.033179208 -3.849693612
## 984 984 1 118.93061 10.11376 9.155902 0.668221077 -0.210345229
## 985 985 1 78.57775 14.09597 5.523923 0.581529382 -0.481916400
## 986 986 1 122.92140 15.52507 1.253460 0.746372288 2.728708307
## 987 987 1 103.83655 15.98425 9.567533 0.054324780 2.282255348
## 988 988 1 74.49775 14.63128 3.766158 0.937235031 -1.805180386
## 989 989 1 75.35345 12.92822 5.102801 0.462610280 -1.686451555
## 990 990 1 68.95041 15.26364 3.309202 0.575918101 -0.807806900
## 991 991 1 91.28304 14.12231 7.051300 0.047195424 -0.023588131
## 992 992 1 122.58400 12.20098 3.082280 0.501901606 -0.361099214
## 993 993 1 84.57114 10.44158 3.234570 0.428048074 2.558755152
## 994 994 1 116.11665 10.11563 9.269568 0.609655731 2.654057727
## 995 995 1 100.96747 14.98359 4.279481 0.040618361 1.003594978
## 996 996 1 99.64842 13.67727 3.460130 0.336970939 1.964597626
## 997 997 1 108.84549 15.89380 3.528101 0.205145500 -1.243980440
## 998 998 1 113.83624 10.85625 3.278173 0.489040898 -4.233866404
## 999 999 1 84.68313 13.84138 6.121114 0.541816804 2.008483621
## 1000 1000 1 71.49173 14.65108 4.611031 0.005188448 1.557143703
## size_centered natural_mortality fishing_mortality total_mortality
## 1 -36.626896493 50.75459 13.662690 64.41728
## 2 -28.586241491 60.75847 12.858624 73.61710
## 3 -18.376486329 50.55845 11.837649 62.39610
## 4 -30.032233114 59.62270 13.003223 72.62592
## 5 -31.511039683 50.18073 13.151104 63.33183
## 6 -15.834645848 46.07224 11.583465 57.65570
## 7 4.160295613 42.00180 9.583970 51.58577
## 8 -5.302848564 45.94503 10.530285 56.47531
## 9 -28.198957194 60.70568 12.819896 73.52558
## 10 -50.097811827 62.59332 15.009781 77.60310
## 11 -44.270822275 54.34212 14.427082 68.76920
## 12 4.171195177 38.69422 9.582880 48.27710
## 13 -53.600839505 69.90934 15.360084 85.26943
## 14 -17.865280048 55.70882 11.786528 67.49535
## 15 -42.849636837 73.46856 14.284964 87.75352
## 16 -0.290409385 37.45765 10.029041 47.48670
## 17 -22.550329473 47.35370 12.255033 59.60874
## 18 -57.050578343 66.42813 15.705058 82.13318
## 19 -48.911496382 65.05044 14.891150 79.94159
## 20 -26.310932497 55.89607 12.631093 68.52717
## 21 -20.720991592 58.52593 12.072099 70.59803
## 22 7.202330534 28.67542 9.279767 37.95519
## 23 5.820500129 40.05339 9.417950 49.47134
## 24 -32.071571127 50.45516 13.207157 63.66232
## 25 -4.142926564 45.46294 10.414293 55.87723
## 26 -49.265003311 73.23709 14.926500 88.16359
## 27 5.628633166 34.10255 9.437137 43.53968
## 28 -3.675568600 45.22087 10.367557 55.58842
## 29 -31.282969438 58.64823 13.128297 71.77653
## 30 -50.317446918 73.14354 15.031745 88.17528
## 31 -25.933498228 50.01844 12.593350 62.61179
## 32 -9.190229089 59.88167 10.919023 70.80070
## 33 -8.864135200 48.26313 10.886414 59.14955
## 34 -57.625599522 67.25252 15.762560 83.01508
## 35 -55.944394227 73.88905 15.594439 89.48349
## 36 0.773562535 40.42230 9.922644 50.34494
## 37 -42.906300647 67.88167 14.290630 82.17230
## 38 -40.769654706 57.85871 14.076965 71.93568
## 39 -6.881958367 53.75864 10.688196 64.44683
## 40 -44.163070626 54.60261 14.416307 69.01892
## 41 -56.128892114 67.60778 15.612889 83.22067
## 42 -57.510638991 67.79178 15.751064 83.54284
## 43 -26.803173947 59.37855 12.680317 72.05887
## 44 -23.405238208 48.02321 12.340524 60.36374
## 45 -53.937071133 74.11798 15.393707 89.51168
## 46 -5.803822691 50.07804 10.580382 60.65842
## 47 -3.479879689 50.95842 10.347988 61.30641
## 48 -33.715068675 65.30895 13.371507 78.68046
## 49 4.234898710 40.39441 9.576510 49.97092
## 50 -2.769654510 52.02318 10.276965 62.30014
## 51 -33.626909808 72.31641 13.362691 85.67910
## 52 -58.077953332 73.02543 15.807795 88.83323
## 53 1.178612218 37.79411 9.882139 47.67625
## 54 -46.740837027 60.32018 14.674084 74.99427
## 55 -18.881204091 58.80127 11.888120 70.68939
## 56 -44.522034435 59.48655 14.452203 73.93876
## 57 -56.079698021 65.82917 15.607970 81.43714
## 58 5.374669945 53.99070 9.462533 63.45323
## 59 -22.073354023 63.42081 12.207335 75.62814
## 60 -57.126126080 62.66279 15.712613 78.37540
## 61 -38.022329053 56.36543 13.802233 70.16766
## 62 -5.002740340 40.29287 10.500274 50.79315
## 63 -23.802245930 53.42339 12.380225 65.80361
## 64 -9.635938064 55.81522 10.963594 66.77882
## 65 -27.885341523 65.14315 12.788534 77.93169
## 66 -0.929166758 53.57906 10.092917 63.67198
## 67 -57.972989383 78.51940 15.797299 94.31670
## 68 -42.786492771 58.04221 14.278649 72.32085
## 69 -20.566339325 46.64701 12.056634 58.70365
## 70 -51.382547468 65.08708 15.138255 80.22534
## 71 1.883145531 37.79507 9.811685 47.60675
## 72 3.158255096 48.65668 9.684174 58.34085
## 73 -43.819728149 62.84178 14.381973 77.22375
## 74 -57.739673108 66.77852 15.773967 82.55249
## 75 -42.265368220 71.40747 14.226537 85.63400
## 76 -33.302258451 63.40782 13.330226 76.73805
## 77 7.836353395 48.16154 9.216365 57.37791
## 78 -3.728857015 40.28376 10.372886 50.65664
## 79 -49.053004016 60.29918 14.905300 75.20448
## 80 -42.392598598 69.74461 14.239260 83.98387
## 81 -10.134639544 47.53596 11.013464 58.54943
## 82 -55.677508956 65.45758 15.567751 81.02533
## 83 -12.052636596 45.81992 11.205264 57.02518
## 84 7.117806333 43.51441 9.288219 52.80263
## 85 -59.866020316 72.84722 15.986602 88.83383
## 86 -33.358678115 51.66830 13.335868 65.00416
## 87 -31.029787012 64.16938 13.102979 77.27236
## 88 -6.756117195 50.03610 10.675612 60.71171
## 89 -32.065432349 57.36233 13.206543 70.56887
## 90 -41.331401519 66.90710 14.133140 81.04024
## 91 -40.387650307 63.10400 14.038765 77.14276
## 92 -54.621078041 66.30497 15.462108 81.76707
## 93 -45.344444832 65.52396 14.534444 80.05841
## 94 -9.117429936 53.60394 10.911743 64.51568
## 95 -26.302411892 53.68302 12.630241 66.31326
## 96 -52.111637963 75.91418 15.211164 91.12535
## 97 -4.014732428 56.14846 10.401473 66.54994
## 98 -52.958207882 63.66390 15.295821 78.95973
## 99 5.201359072 41.69666 9.479864 51.17652
## 100 3.260230504 38.09196 9.673977 47.76594
## 101 -27.940274454 50.74178 12.794027 63.53580
## 102 -53.460581466 57.04467 15.346058 72.39073
## 103 -44.846921919 61.76818 14.484692 76.25287
## 104 -25.160359372 55.02569 12.516036 67.54173
## 105 -23.303843569 49.70320 12.330384 62.03359
## 106 -30.775143751 64.90735 13.077514 77.98487
## 107 -29.239013689 55.92499 12.923901 68.84890
## 108 -26.244630078 54.32558 12.624463 66.95004
## 109 -6.901516484 55.72724 10.690152 66.41740
## 110 -16.168145011 44.95990 11.616815 56.57672
## 111 -44.058360700 69.36172 14.405836 83.76756
## 112 -31.088710120 46.61915 13.108871 59.72802
## 113 0.663830661 39.63334 9.933617 49.56695
## 114 -15.739474851 50.80532 11.573947 62.37927
## 115 7.246398763 45.47063 9.275360 54.74599
## 116 -37.692286482 52.62762 13.769229 66.39685
## 117 -23.749046666 48.48502 12.374905 60.85992
## 118 -5.311174130 47.06875 10.531117 57.59987
## 119 -0.762804013 49.37955 10.076280 59.45583
## 120 -38.183728002 68.81182 13.818373 82.63019
## 121 -22.635128265 61.19334 12.263513 73.45686
## 122 1.867909732 36.00581 9.813209 45.81901
## 123 -43.231676521 58.39267 14.323168 72.71584
## 124 -11.043419337 53.03937 11.104342 64.14372
## 125 -9.968681482 47.13580 10.996868 58.13267
## 126 -56.045487823 60.95557 15.604549 76.56012
## 127 -41.158533141 55.28156 14.115853 69.39741
## 128 -14.247875086 57.04377 11.424788 68.46856
## 129 -23.168554411 47.48992 12.316855 59.80678
## 130 -45.594771106 70.07432 14.559477 84.63379
## 131 -18.331725788 44.45276 11.833173 56.28593
## 132 -53.047628193 76.37439 15.304763 91.67916
## 133 9.072353279 40.11668 9.092765 49.20945
## 134 -25.452549648 53.55449 12.545255 66.09974
## 135 -0.487135737 50.60877 10.048714 60.65749
## 136 -41.832333710 63.03368 14.183233 77.21692
## 137 -41.209815613 55.92855 14.120982 70.04954
## 138 1.684042339 36.97536 9.831596 46.80696
## 139 -39.286302910 51.18171 13.928630 65.11034
## 140 -25.764434864 65.79512 12.576443 78.37156
## 141 3.505800620 30.20604 9.649420 39.85546
## 142 -33.601015608 63.29953 13.360102 76.65963
## 143 -25.083868999 66.76208 12.508387 79.27047
## 144 -20.905264320 48.32063 12.090526 60.41116
## 145 -29.317860855 48.82381 12.931786 61.75560
## 146 -50.417686524 68.05811 15.041769 83.09988
## 147 -12.655989688 57.25338 11.265599 68.51898
## 148 -5.204029977 51.85307 10.520403 62.37347
## 149 -0.913019860 48.36969 10.091302 58.46099
## 150 -16.042578756 53.07349 11.604258 64.67775
## 151 -28.990977239 63.50068 12.899098 76.39977
## 152 -28.126417280 48.56556 12.812642 61.37820
## 153 -46.146107544 68.17508 14.614611 82.78969
## 154 -52.546830885 64.59279 15.254683 79.84747
## 155 -25.996767220 64.56219 12.599677 77.16186
## 156 -39.526925986 51.76063 13.952693 65.71332
## 157 -41.118535406 55.35085 14.111854 69.46271
## 158 6.332003183 42.46161 9.366800 51.82841
## 159 -41.524419799 61.24892 14.152442 75.40136
## 160 -16.618645624 55.02682 11.661865 66.68868
## 161 5.044525901 36.65711 9.495547 46.15266
## 162 -38.540714390 50.91693 13.854071 64.77100
## 163 5.022362852 42.38112 9.497764 51.87888
## 164 -20.010275235 56.06112 12.001028 68.06215
## 165 -9.234394617 55.21160 10.923439 66.13504
## 166 -8.816489414 51.75274 10.881649 62.63439
## 167 -22.126479896 53.69159 12.212648 65.90424
## 168 5.874473294 38.75931 9.412553 48.17187
## 169 -41.173047796 66.61496 14.117305 80.73226
## 170 -19.562070591 53.90493 11.956207 65.86114
## 171 -2.028519735 43.08987 10.202852 53.29272
## 172 -50.288918286 51.57393 15.028892 66.60283
## 173 -3.035070633 39.60870 10.303507 49.91221
## 174 9.808755952 46.89415 9.019124 55.91327
## 175 -26.597200548 42.10484 12.659720 54.76456
## 176 2.781800102 37.77272 9.721820 47.49454
## 177 -14.448128666 42.75559 11.444813 54.20040
## 178 -32.598333890 53.89729 13.259833 67.15713
## 179 -51.099077384 59.67623 15.109908 74.78614
## 180 -19.693609334 50.91227 11.969361 62.88163
## 181 -11.623435165 44.05454 11.162344 55.21688
## 182 -2.481289571 38.93486 10.248129 49.18298
## 183 -49.777224283 70.66577 14.977722 85.64349
## 184 0.700712353 43.53605 9.929929 53.46597
## 185 -16.707653576 48.31511 11.670765 59.98588
## 186 -42.197407889 59.09123 14.219741 73.31097
## 187 1.318795416 51.58293 9.868120 61.45105
## 188 -48.540900375 63.33023 14.854090 78.18432
## 189 -58.293781828 68.38193 15.829378 84.21131
## 190 -13.077653847 43.29173 11.307765 54.59950
## 191 6.131035320 38.86469 9.386896 48.25159
## 192 4.214556115 37.49232 9.578544 47.07087
## 193 -50.407377458 62.07110 15.040738 77.11183
## 194 -33.266707812 57.03311 13.326671 70.35978
## 195 -6.337861158 44.91102 10.633786 55.54481
## 196 8.445668137 47.69660 9.155433 56.85203
## 197 -54.180934655 59.80953 15.418093 75.22762
## 198 6.086524352 40.28172 9.391348 49.67307
## 199 -38.769268608 55.13436 13.876927 69.01129
## 200 -10.893898834 39.82664 11.089390 50.91603
## 201 -29.681374927 63.95998 12.968137 76.92812
## 202 6.962258939 42.25762 9.303774 51.56140
## 203 -10.064190372 45.68542 11.006419 56.69184
## 204 -54.271044605 62.44615 15.427104 77.87325
## 205 -23.386361843 57.35997 12.338636 69.69861
## 206 -1.135935572 47.51386 10.113594 57.62745
## 207 -39.716301565 59.11135 13.971630 73.08298
## 208 -46.105115265 63.52815 14.610512 78.13866
## 209 0.295402308 37.26893 9.970460 47.23939
## 210 -6.178405420 47.13828 10.617841 57.75612
## 211 -48.432995360 67.37734 14.843300 82.22064
## 212 -43.356303254 64.84932 14.335630 79.18496
## 213 -21.321185045 47.48111 12.132119 59.61323
## 214 -12.984560065 57.30347 11.298456 68.60193
## 215 -23.102285159 46.53075 12.310229 58.84098
## 216 -4.531441811 41.42263 10.453144 51.87577
## 217 -47.573842735 70.97494 14.757384 85.73232
## 218 -44.495141110 56.53874 14.449514 70.98826
## 219 -40.032557666 63.84527 14.003256 77.84853
## 220 8.106381958 50.53325 9.189362 59.72261
## 221 -29.998367035 51.85213 12.999837 64.85197
## 222 -41.426620807 60.79104 14.142662 74.93370
## 223 7.907571383 53.70179 9.209243 62.91103
## 224 -3.433155206 38.22100 10.343316 48.56432
## 225 -42.555707076 61.59264 14.255571 75.84821
## 226 -13.206441724 51.75977 11.320644 63.08041
## 227 -56.492459644 66.62741 15.649246 82.27665
## 228 -31.263756696 58.75445 13.126376 71.88082
## 229 -45.146762349 60.60471 14.514676 75.11939
## 230 -26.568965674 63.67424 12.656897 76.33113
## 231 5.917004542 51.62362 9.408300 61.03192
## 232 -10.423990244 53.61805 11.042399 64.66045
## 233 -32.699581161 56.54077 13.269958 69.81073
## 234 -46.928052793 69.63336 14.692805 84.32617
## 235 -3.451578221 41.04753 10.345158 51.39269
## 236 -47.211900554 68.74173 14.721190 83.46292
## 237 -3.096183739 51.54007 10.309618 61.84968
## 238 -15.107952598 50.39392 11.510795 61.90471
## 239 -48.442356575 64.86463 14.844236 79.70887
## 240 -28.806762418 57.17097 12.880676 70.05165
## 241 7.036319373 30.11236 9.296368 39.40873
## 242 3.526547279 38.74206 9.647345 48.38940
## 243 -51.617567877 63.18128 15.161757 78.34304
## 244 -4.764400488 50.52622 10.476440 61.00266
## 245 -17.759266009 46.34639 11.775927 58.12231
## 246 -43.313393123 54.13169 14.331339 68.46303
## 247 -34.814933788 49.72086 13.481493 63.20236
## 248 9.527274829 36.43928 9.047273 45.48655
## 249 -23.934090394 47.65723 12.393409 60.05064
## 250 -43.440677642 60.50870 14.344068 74.85277
## 251 -14.242316864 55.07151 11.424232 66.49574
## 252 -32.359217382 59.86290 13.235922 73.09882
## 253 -23.424558796 57.25903 12.342456 69.60148
## 254 -17.397882154 52.69924 11.739788 64.43903
## 255 -17.851216949 60.53308 11.785122 72.31820
## 256 -27.530454679 57.92405 12.753045 70.67710
## 257 -24.552257343 49.72662 12.455226 62.18184
## 258 -55.870799415 58.87327 15.587080 74.46035
## 259 -33.525364508 47.04175 13.352536 60.39428
## 260 5.213849726 41.08247 9.478615 50.56109
## 261 -3.709878363 55.64328 10.370988 66.01427
## 262 -32.263010100 57.39502 13.226301 70.62132
## 263 1.811610789 32.70351 9.818839 42.52235
## 264 -3.490751497 57.28628 10.349075 67.63536
## 265 -18.070659868 47.36088 11.807066 59.16794
## 266 -42.394746270 71.40287 14.239475 85.64234
## 267 -59.531842531 69.64278 15.953184 85.59596
## 268 -18.402026207 58.18295 11.840203 70.02315
## 269 -18.742743200 55.95553 11.874274 67.82981
## 270 -2.791602651 50.35625 10.279160 60.63541
## 271 6.457566146 37.14893 9.354243 46.50317
## 272 -14.388143995 49.73912 11.438814 61.17793
## 273 -32.200382783 54.06951 13.220038 67.28955
## 274 -32.983011331 57.60862 13.298301 70.90692
## 275 -36.159462531 55.72925 13.615946 69.34520
## 276 -34.490888608 52.97031 13.449089 66.41940
## 277 -2.213605789 47.35003 10.221361 57.57139
## 278 -58.344018350 67.36584 15.834402 83.20024
## 279 -15.952689955 45.36394 11.595269 56.95921
## 280 -13.083358426 46.88040 11.308336 58.18873
## 281 -12.464380139 44.70551 11.246438 55.95195
## 282 -20.410606784 57.18179 12.041061 69.22285
## 283 -45.511540961 59.90322 14.551154 74.45438
## 284 -20.490946486 51.95918 12.049095 64.00827
## 285 -55.217178883 63.09747 15.521718 78.61918
## 286 -17.983090146 55.92244 11.798309 67.72075
## 287 9.115256206 38.31145 9.088474 47.39992
## 288 -14.051484100 50.72598 11.405148 62.13113
## 289 -9.721338926 46.28850 10.972134 57.26063
## 290 -41.430129814 60.46030 14.143013 74.60331
## 291 4.928469385 47.53613 9.507153 57.04328
## 292 3.136365970 42.39832 9.686363 52.08469
## 293 -28.510284328 63.34132 12.851028 76.19234
## 294 4.939942318 41.17258 9.506006 50.67859
## 295 6.070150894 38.01512 9.392985 47.40811
## 296 -29.450664138 63.40806 12.945066 76.35313
## 297 9.592006139 41.70227 9.040799 50.74307
## 298 -34.024448360 57.16959 13.402445 70.57203
## 299 -36.925558110 66.39488 13.692556 80.08744
## 300 -31.684414721 61.41644 13.168441 74.58488
## 301 -38.597633706 49.57916 13.859763 63.43892
## 302 -15.905242567 46.73410 11.590524 58.32462
## 303 -23.025800751 50.89726 12.302580 63.19984
## 304 6.425043051 43.01311 9.357496 52.37061
## 305 -51.649146478 55.97738 15.164915 71.14230
## 306 -22.827850212 49.00483 12.282785 61.28761
## 307 -33.769588235 63.98390 13.376959 77.36086
## 308 2.902728687 37.45838 9.709727 47.16811
## 309 -54.869070568 63.84373 15.486907 79.33064
## 310 4.167479770 34.70246 9.583252 44.28571
## 311 -59.898653473 60.84636 15.989865 76.83622
## 312 9.803011753 45.23358 9.019699 54.25328
## 313 -34.806689371 63.13485 13.480669 76.61552
## 314 -12.101461960 49.47482 11.210146 60.68496
## 315 -22.884664617 48.48542 12.288466 60.77388
## 316 -44.408074366 64.15599 14.440807 78.59680
## 317 -55.424365303 67.01546 15.542437 82.55790
## 318 -49.009616871 71.28808 14.900962 86.18904
## 319 -39.700144546 58.50716 13.970014 72.47717
## 320 7.886060863 36.99113 9.211394 46.20252
## 321 -17.189896358 56.12425 11.718990 67.84324
## 322 -22.903641020 54.01092 12.290364 66.30128
## 323 -2.504319192 38.84577 10.250432 49.09620
## 324 -32.485832048 61.21515 13.248583 74.46374
## 325 -20.871046446 60.90978 12.087105 72.99689
## 326 -30.241082467 47.05465 13.024108 60.07876
## 327 -11.144741091 49.02879 11.114474 60.14326
## 328 -8.966564902 45.45616 10.896656 56.35282
## 329 -29.663641485 69.32111 12.966364 82.28748
## 330 -47.385715349 69.64025 14.738572 84.37882
## 331 -28.459382011 47.77688 12.845938 60.62281
## 332 -38.709822737 54.75495 13.870982 68.62593
## 333 -9.010990956 38.66511 10.901099 49.56621
## 334 -23.947149315 47.47652 12.394715 59.87123
## 335 -12.089770599 41.53159 11.208977 52.74057
## 336 -58.859772531 69.16315 15.885977 85.04913
## 337 -10.787438927 58.37365 11.078744 69.45240
## 338 -7.147381108 50.81369 10.714738 61.52843
## 339 -5.192275527 44.15353 10.519228 54.67276
## 340 -3.420229000 44.60006 10.342023 54.94208
## 341 -21.780916161 51.21529 12.178092 63.39338
## 342 -13.834533151 41.58913 11.383453 52.97258
## 343 -49.478417237 56.71686 14.947842 71.66470
## 344 -28.894327870 54.86698 12.889433 67.75641
## 345 -25.889904732 44.87384 12.588990 57.46283
## 346 6.282009943 36.94112 9.371799 46.31292
## 347 -3.084951025 39.17988 10.308495 49.48838
## 348 -24.681304148 55.80892 12.468130 68.27705
## 349 -58.976835262 71.47616 15.897684 87.37385
## 350 -29.091599965 56.85424 12.909160 69.76340
## 351 -8.260312721 48.89319 10.826031 59.71922
## 352 -38.976597115 61.12170 13.897660 75.01936
## 353 -7.696568505 44.10121 10.769657 54.87086
## 354 -7.641281970 54.26572 10.764128 65.02985
## 355 -54.207226562 67.29298 15.420723 82.71371
## 356 -41.679501669 60.20309 14.167950 74.37104
## 357 -57.191187134 69.80242 15.719119 85.52154
## 358 -51.317689065 61.87493 15.131769 77.00670
## 359 -8.122839448 52.71281 10.812284 63.52509
## 360 -24.223481137 50.09774 12.422348 62.52009
## 361 -45.605686919 70.76070 14.560569 85.32127
## 362 -45.636544051 62.66832 14.563654 77.23197
## 363 -44.496998822 67.35224 14.449700 81.80194
## 364 -29.266065676 58.28407 12.926607 71.21068
## 365 -35.405914811 66.87298 13.540591 80.41357
## 366 -47.379168351 56.24424 14.737917 70.98216
## 367 -42.088748971 50.91294 14.208875 65.12181
## 368 -39.007887859 57.22225 13.900789 71.12304
## 369 -5.695623169 41.24674 10.569562 51.81631
## 370 -2.246019214 53.71066 10.224602 63.93526
## 371 4.844435579 41.18840 9.515556 50.70396
## 372 -9.631623439 45.00392 10.963162 55.96708
## 373 -14.469148873 48.96345 11.446915 60.41036
## 374 -42.823863472 69.83587 14.282386 84.11826
## 375 9.761752167 36.31450 9.023825 45.33833
## 376 -3.550708592 42.66713 10.355071 53.02220
## 377 -31.062557269 52.12899 13.106256 65.23525
## 378 -34.335148130 56.60594 13.433515 70.03945
## 379 -31.708688608 55.09202 13.170869 68.26289
## 380 -55.064265872 73.32897 15.506427 88.83539
## 381 -9.972947212 52.81349 10.997295 63.81079
## 382 -14.193754015 53.57931 11.419375 64.99868
## 383 -27.763650087 60.07697 12.776365 72.85333
## 384 -8.386745614 42.45471 10.838675 53.29339
## 385 -33.456453881 60.75489 13.345645 74.10053
## 386 -24.331553762 59.29155 12.433155 71.72470
## 387 5.434490102 36.22150 9.456551 45.67805
## 388 -12.025015070 53.42205 11.202502 64.62455
## 389 -53.415607337 64.27115 15.341561 79.61271
## 390 -40.656512608 61.85237 14.065651 75.91802
## 391 -10.060862796 48.44604 11.006086 59.45213
## 392 -20.650452031 53.78202 12.065045 65.84707
## 393 -29.289459300 66.89978 12.928946 79.82873
## 394 -38.978508040 68.76396 13.897851 82.66181
## 395 -44.275406047 53.06371 14.427541 67.49125
## 396 9.010911798 39.46773 9.098909 48.56664
## 397 -49.478714825 59.72296 14.947871 74.67083
## 398 -53.895711689 67.95949 15.389571 83.34906
## 399 -3.804134952 50.37550 10.380413 60.75592
## 400 -39.851972507 50.34103 13.985197 64.32623
## 401 -21.351195700 61.63583 12.135120 73.77095
## 402 4.188844813 49.99208 9.581116 59.57320
## 403 7.281468590 34.99974 9.271853 44.27160
## 404 3.641803018 36.46846 9.635820 46.10428
## 405 -41.523076359 69.40379 14.152308 83.55610
## 406 -19.104987646 48.38636 11.910499 60.29686
## 407 -49.697387281 62.85975 14.969739 77.82949
## 408 -56.860968608 64.67100 15.686097 80.35710
## 409 -18.353164303 62.53798 11.835316 74.37329
## 410 -16.440689520 59.77716 11.644069 71.42123
## 411 -37.457691862 59.69600 13.745769 73.44177
## 412 -15.258183228 52.30004 11.525818 63.82586
## 413 -29.583784519 48.11582 12.958378 61.07419
## 414 -17.186738593 47.48379 11.718674 59.20246
## 415 -43.529610427 65.81727 14.352961 80.17024
## 416 -30.615596874 45.71511 13.061560 58.77667
## 417 -23.978634838 46.43423 12.397863 58.83209
## 418 -49.076996874 64.10997 14.907700 79.01767
## 419 -40.892625530 69.44875 14.089263 83.53801
## 420 -8.104352430 44.60225 10.810435 55.41268
## 421 -7.043816794 53.79040 10.704382 64.49479
## 422 0.045908575 43.94905 9.995409 53.94446
## 423 -6.719212083 44.73399 10.671921 55.40591
## 424 9.964022497 34.76395 9.003598 43.76755
## 425 -26.614043654 53.25960 12.661404 65.92100
## 426 -54.710668277 63.50399 15.471067 78.97505
## 427 -29.272292056 54.90895 12.927229 67.83618
## 428 -35.358073204 59.97764 13.535807 73.51345
## 429 -9.283078448 48.94951 10.928308 59.87782
## 430 -5.276667844 41.39719 10.527667 51.92486
## 431 9.136572697 33.33424 9.086343 42.42059
## 432 9.511895687 36.25276 9.048810 45.30157
## 433 8.918627708 36.03061 9.108137 45.13875
## 434 -25.555579823 49.14464 12.555558 61.70020
## 435 -11.990882044 39.59333 11.199088 50.79242
## 436 -44.767768495 62.01591 14.476777 76.49268
## 437 -30.641572450 55.44962 13.064157 68.51378
## 438 5.242961147 43.96374 9.475704 53.43945
## 439 -42.281738762 59.99467 14.228174 74.22284
## 440 7.221752431 43.34000 9.277825 52.61782
## 441 -1.994527932 43.15643 10.199453 53.35589
## 442 -48.308667617 57.26825 14.830867 72.09912
## 443 -47.901435206 65.56820 14.790144 80.35834
## 444 -52.710543633 68.26062 15.271054 83.53168
## 445 -18.439677774 54.75048 11.843968 66.59445
## 446 -39.432431883 51.87522 13.943243 65.81847
## 447 -34.251995825 62.30359 13.425200 75.72879
## 448 -51.439882126 62.70610 15.143988 77.85009
## 449 -24.920798871 48.92553 12.492080 61.41761
## 450 5.344433903 45.56781 9.465557 55.03336
## 451 -14.065775552 48.65679 11.406578 60.06337
## 452 -22.877748075 56.04538 12.287775 68.33315
## 453 -59.926613967 67.19271 15.992661 83.18537
## 454 -28.904431676 59.37579 12.890443 72.26623
## 455 -17.083053412 58.23440 11.708305 69.94271
## 456 8.313109537 44.68993 9.168689 53.85862
## 457 -17.376654781 52.37321 11.737665 64.11088
## 458 2.426583220 37.70283 9.757342 47.46017
## 459 -28.724874686 62.15391 12.872487 75.02640
## 460 -41.069041721 65.14592 14.106904 79.25283
## 461 -9.468095056 60.00517 10.946810 70.95198
## 462 -13.401323843 58.60716 11.340132 69.94729
## 463 3.508759239 43.25991 9.649124 52.90903
## 464 -20.878820776 46.41142 12.087882 58.49930
## 465 -5.238646814 42.91005 10.523865 53.43392
## 466 -45.135711131 65.13504 14.513571 79.64861
## 467 -57.727113822 72.90730 15.772711 88.68002
## 468 -12.643546071 44.22514 11.264355 55.48950
## 469 -45.606887636 65.28808 14.560689 79.84877
## 470 -15.564686339 48.74403 11.556469 60.30050
## 471 -21.904625830 51.03860 12.190463 63.22906
## 472 -57.986274816 72.85884 15.798627 88.65747
## 473 7.012774111 47.26274 9.298723 56.56147
## 474 -59.371057076 66.81118 15.937106 82.74829
## 475 -39.788147195 71.26523 13.978815 85.24404
## 476 -22.904225341 51.21872 12.290423 63.50914
## 477 -36.622179353 61.75342 13.662218 75.41564
## 478 -15.238588441 53.55131 11.523859 65.07517
## 479 -31.519028740 60.89256 13.151903 74.04446
## 480 -48.281498544 71.91754 14.828150 86.74569
## 481 -25.235540287 43.27763 12.523554 55.80118
## 482 8.856320470 40.03939 9.114368 49.15376
## 483 -57.547282029 70.67942 15.754728 86.43414
## 484 -28.459048665 63.56447 12.845905 76.41037
## 485 2.021494748 37.17654 9.797851 46.97439
## 486 3.992364595 41.43097 9.600764 51.03174
## 487 -37.994396689 55.24059 13.799440 69.04003
## 488 -22.462782455 43.95557 12.246278 56.20185
## 489 -56.322586392 68.46828 15.632259 84.10054
## 490 -48.968346757 61.05924 14.896835 75.95607
## 491 -45.116393315 63.07535 14.511639 77.58699
## 492 -23.252000848 52.11236 12.325200 64.43756
## 493 4.066242115 43.22619 9.593376 52.81956
## 494 8.862187199 36.70678 9.113781 45.82056
## 495 -18.327689895 58.60564 11.832769 70.43841
## 496 5.476116950 42.15144 9.452388 51.60383
## 497 -53.987731016 56.01417 15.398773 71.41294
## 498 -43.389233542 69.03450 14.338923 83.37342
## 499 9.308047551 37.22290 9.069195 46.29210
## 500 -4.007434151 50.41320 10.400743 60.81394
## 501 58.661797284 24.93143 53.464719 78.39615
## 502 48.935653346 22.62581 49.574261 72.20007
## 503 11.175551186 33.32413 34.470220 67.79435
## 504 46.491174104 26.95106 48.596470 75.54753
## 505 50.407211070 24.51392 50.162884 74.67680
## 506 54.446202514 16.89160 51.778481 68.67008
## 507 16.308191288 38.01703 36.523277 74.54031
## 508 -7.133527067 48.78162 27.146589 75.92821
## 509 55.614122765 20.93016 52.245649 73.17581
## 510 57.669875096 28.30307 53.067950 81.37102
## 511 30.485108725 42.10018 42.194043 84.29422
## 512 5.368114959 48.93142 32.147246 81.07866
## 513 1.397049229 41.47497 30.558820 72.03379
## 514 -2.452633490 48.24794 29.018947 77.26688
## 515 1.248887437 52.45056 30.499555 82.95012
## 516 8.290664740 33.61464 33.316266 66.93091
## 517 21.077678518 34.46845 38.431071 72.89952
## 518 -7.444312288 41.14573 27.022275 68.16801
## 519 -9.220320259 47.73871 26.311872 74.05058
## 520 3.212430845 50.08806 31.284972 81.37303
## 521 18.719644034 38.85150 37.487858 76.33936
## 522 11.731418525 27.71370 34.692567 62.40627
## 523 38.550828840 25.83770 45.420332 71.25803
## 524 29.132819278 41.07451 41.653128 82.72763
## 525 24.944225498 28.70902 39.977690 68.68671
## 526 21.600962784 41.00772 38.640385 79.64811
## 527 40.379835151 31.36150 46.151934 77.51343
## 528 -3.712113444 50.83901 28.515155 79.35417
## 529 52.055592178 27.02502 50.822237 77.84726
## 530 31.884317696 38.65337 42.753727 81.40710
## 531 37.637846440 23.12301 45.055139 68.17815
## 532 12.614593883 38.89561 35.045838 73.94145
## 533 33.368961038 33.40685 43.347584 76.75443
## 534 0.773476805 39.47848 30.309391 69.78787
## 535 -1.819989877 47.01553 29.272004 76.28753
## 536 11.242112599 43.34820 34.496845 77.84504
## 537 47.156660045 32.60230 48.862664 81.46497
## 538 14.673160790 45.88870 35.869264 81.75797
## 539 16.736138479 38.53831 36.694455 75.23277
## 540 12.914373537 42.32674 35.165749 77.49249
## 541 54.511243994 21.16167 51.804498 72.96617
## 542 55.708895533 21.02686 52.283558 73.31042
## 543 18.471409497 39.06232 37.388564 76.45089
## 544 53.102590395 28.55204 51.241036 79.79308
## 545 38.772379842 23.84422 45.508952 69.35317
## 546 -9.636993143 46.87989 26.145203 73.02509
## 547 3.418869474 39.97975 31.367548 71.34730
## 548 26.325047668 37.32374 40.530019 77.85376
## 549 10.485312976 28.07295 34.194125 62.26708
## 550 46.280103151 25.78180 48.512041 74.29384
## 551 -9.834403773 43.60390 26.066238 69.67014
## 552 29.532524408 34.09584 41.813010 75.90884
## 553 -6.713796814 45.94950 27.314481 73.26398
## 554 5.309751546 49.69913 32.123901 81.82303
## 555 46.169148411 12.30580 48.467659 60.77346
## 556 18.630159721 35.82025 37.452064 73.27232
## 557 0.083816657 44.70944 30.033527 74.74297
## 558 -8.582542338 46.63057 26.566983 73.19755
## 559 39.502404546 28.09194 45.800962 73.89290
## 560 -1.619414131 35.93230 29.352234 65.28454
## 561 41.007277179 24.55245 46.402911 70.95536
## 562 34.429928167 26.41897 43.771971 70.19094
## 563 38.736602822 36.17756 45.494641 81.67220
## 564 21.500695178 25.26026 38.600278 63.86053
## 565 40.602626051 31.79247 46.241050 78.03352
## 566 1.524338606 42.78509 30.609735 73.39483
## 567 14.762168399 24.91393 35.904867 60.81879
## 568 2.822578254 43.74822 31.129031 74.87725
## 569 15.798200881 27.84152 36.319280 64.16080
## 570 18.196282743 36.45712 37.278513 73.73563
## 571 26.648840308 39.35864 40.659536 80.01818
## 572 2.987900379 35.02644 31.195160 66.22160
## 573 16.873922981 29.01098 36.749569 65.76055
## 574 2.693965614 38.40753 31.077586 69.48512
## 575 58.660954328 12.34555 53.464382 65.80993
## 576 -0.501249330 40.47497 29.799500 70.27447
## 577 41.602464574 26.59780 46.640986 73.23879
## 578 14.297821631 40.22797 35.719129 75.94710
## 579 33.996972230 26.91412 43.598789 70.51291
## 580 30.148334401 33.72075 42.059334 75.78009
## 581 16.829769204 45.65916 36.731908 82.39106
## 582 13.809373053 43.11052 35.523749 78.63427
## 583 37.427728896 24.50968 44.971092 69.48077
## 584 35.233973456 39.09055 44.093589 83.18414
## 585 54.669967440 25.04378 51.867987 76.91177
## 586 0.512135918 43.45491 30.204854 73.65977
## 587 55.606643024 21.30211 52.242657 73.54477
## 588 -2.999313027 40.51799 28.800275 69.31826
## 589 59.136883975 16.94291 53.654754 70.59767
## 590 44.816066173 31.71063 47.926426 79.63706
## 591 30.100453368 33.00496 42.040181 75.04514
## 592 32.665909030 19.22899 43.066364 62.29535
## 593 52.993560710 12.94425 51.197424 64.14168
## 594 7.210964882 40.62843 32.884386 73.51282
## 595 31.728462903 38.74882 42.691385 81.44020
## 596 31.619454715 27.24640 42.647782 69.89418
## 597 -5.149374004 40.80892 27.940250 68.74917
## 598 52.761712475 17.50166 51.104685 68.60634
## 599 35.666869220 32.19212 44.266748 76.45886
## 600 51.558369754 31.24599 50.623348 81.86934
## 601 42.947229478 30.59874 47.178892 77.77763
## 602 38.788304776 38.63170 45.515322 84.14703
## 603 46.378857833 23.04102 48.551543 71.59257
## 604 -1.884159015 37.58336 29.246336 66.82970
## 605 45.814584694 27.44617 48.325834 75.77201
## 606 38.802756912 23.11316 45.521103 68.63426
## 607 54.312322396 26.21605 51.724929 77.94098
## 608 30.478900305 26.54977 42.191560 68.74133
## 609 14.792922933 33.47151 35.917169 69.38868
## 610 24.806741241 34.16181 39.922696 74.08451
## 611 49.109024098 20.09372 49.643610 69.73733
## 612 58.398802935 24.90971 53.359521 78.26924
## 613 21.754505604 32.69491 38.701802 71.39671
## 614 58.100387729 16.22376 53.240155 69.46392
## 615 9.937807792 37.60154 33.975123 71.57666
## 616 19.675829231 44.16649 37.870332 82.03682
## 617 -3.010980054 45.95760 28.795608 74.75321
## 618 26.277591251 38.79718 40.511037 79.30821
## 619 29.273589340 24.24476 41.709436 65.95420
## 620 13.316957082 42.07039 35.326783 77.39717
## 621 30.704852182 36.58594 42.281941 78.86788
## 622 9.639261484 44.81286 33.855705 78.66857
## 623 -9.997234889 50.80008 26.001106 76.80119
## 624 47.001125657 29.56438 48.800450 78.36483
## 625 35.697940607 30.27002 44.279176 74.54919
## 626 -2.261464919 40.15841 29.095414 69.25382
## 627 16.291107198 45.37107 36.516443 81.88751
## 628 6.853332534 39.36540 32.741333 72.10674
## 629 47.469218487 23.18211 48.987687 72.16980
## 630 -1.135978259 39.20553 29.545609 68.75114
## 631 32.497499760 28.68594 42.999000 71.68494
## 632 50.543975618 22.10697 50.217590 72.32456
## 633 55.118968005 28.15158 52.047587 80.19917
## 634 54.370021953 17.77473 51.748009 69.52274
## 635 43.442608712 28.38762 47.377043 75.76466
## 636 21.359380661 30.43608 38.543752 68.97984
## 637 30.944686835 32.93526 42.377875 75.31313
## 638 18.446887520 34.51004 37.378755 71.88879
## 639 3.606899234 45.41653 31.442760 76.85929
## 640 -1.010072529 41.68920 29.595971 71.28517
## 641 1.372325644 43.67097 30.548930 74.21990
## 642 27.750192774 31.37310 41.100077 72.47318
## 643 52.415315220 29.98001 50.966126 80.94613
## 644 0.938489884 42.93473 30.375396 73.31012
## 645 17.833936401 39.63269 37.133575 76.76626
## 646 25.534658872 44.09555 40.213864 84.30941
## 647 44.924682993 33.94355 47.969873 81.91342
## 648 50.517470906 34.27732 50.206988 84.48430
## 649 -2.941358192 51.98907 28.823457 80.81252
## 650 -5.693742121 42.91663 27.722503 70.63913
## 651 8.565475098 39.49163 33.426190 72.91782
## 652 25.525712690 40.53423 40.210285 80.74451
## 653 37.185053395 28.17412 44.874021 73.04814
## 654 49.375076289 23.96214 49.750031 73.71217
## 655 10.520821614 37.05466 34.208329 71.26299
## 656 18.853312277 38.05199 37.541325 75.59332
## 657 24.611897911 32.23065 39.844759 72.07541
## 658 36.671110850 35.42186 44.668444 80.09031
## 659 50.046745078 19.02965 50.018698 69.04834
## 660 12.292874644 34.68331 34.917150 69.60046
## 661 54.709568641 28.29194 51.883827 80.17577
## 662 55.227787003 26.83073 52.091115 78.92184
## 663 52.866844686 18.56127 51.146738 69.70801
## 664 37.673345446 24.52643 45.069338 69.59577
## 665 -3.596650702 49.68448 28.561340 78.24582
## 666 13.175868702 33.72855 35.270347 68.99890
## 667 42.324181951 27.19771 46.929673 74.12738
## 668 27.595990677 32.91300 41.038396 73.95140
## 669 43.723294241 36.97170 47.489318 84.46102
## 670 13.575731695 41.63342 35.430293 77.06371
## 671 32.182215697 38.28553 42.872886 81.15841
## 672 54.836292814 19.76011 51.934517 71.69463
## 673 36.817849716 22.89089 44.727140 67.61803
## 674 41.718387560 25.99935 46.687355 72.68671
## 675 9.973385176 37.01484 33.989354 71.00419
## 676 -4.616710090 38.02256 28.153316 66.17587
## 677 28.553590211 36.15000 41.421436 77.57144
## 678 20.040461731 31.55566 38.016185 69.57184
## 679 6.781046691 44.12252 32.712419 76.83494
## 680 26.737952747 33.07791 40.695181 73.77309
## 681 -7.086414476 36.64969 27.165434 63.81512
## 682 10.646816201 32.42951 34.258726 66.68823
## 683 0.744075261 49.51618 30.297630 79.81381
## 684 54.656878677 23.01596 51.862751 74.87872
## 685 -4.362420433 43.58993 28.255032 71.84497
## 686 59.536681792 19.83731 53.814673 73.65198
## 687 -9.130863179 41.31993 26.347655 67.66758
## 688 2.654891952 47.34865 31.061957 78.41060
## 689 55.842467209 29.47370 52.336987 81.81069
## 690 2.612206915 51.02606 31.044883 82.07094
## 691 41.903881931 19.67201 46.761553 66.43356
## 692 24.172291777 30.90924 39.668917 70.57815
## 693 17.119122364 41.66605 36.847649 78.51370
## 694 -9.500753460 38.25314 26.199699 64.45284
## 695 39.089961341 23.03467 45.635985 68.67065
## 696 46.033077708 25.27286 48.413231 73.68609
## 697 -0.004846442 47.43831 29.998061 77.43637
## 698 50.860603268 22.62727 50.344241 72.97151
## 699 21.740058619 44.20305 38.696023 82.89908
## 700 27.766389642 32.71639 41.106556 73.82294
## 701 5.849816839 38.40919 32.339927 70.74911
## 702 23.599626787 35.45660 39.439851 74.89645
## 703 -3.234379755 47.24264 28.706248 75.94889
## 704 7.267164765 41.58779 32.906866 74.49465
## 705 58.686222353 21.73985 53.474489 75.21434
## 706 3.615782831 41.07679 31.446313 72.52310
## 707 54.184220165 18.27865 51.673688 69.95234
## 708 43.161858544 25.90424 47.264743 73.16899
## 709 -9.105166220 44.76545 26.357934 71.12338
## 710 32.887274087 36.07607 43.154910 79.23098
## 711 20.442302309 37.23670 38.176921 75.41362
## 712 30.150400843 33.11442 42.060160 75.17459
## 713 30.453063899 37.06513 42.181226 79.24636
## 714 45.422344408 25.64732 48.168938 73.81626
## 715 29.685309625 30.16744 41.874124 72.04156
## 716 -8.126900296 61.22303 26.749240 87.97227
## 717 22.213790868 31.43895 38.885516 70.32447
## 718 43.081677423 16.40036 47.232671 63.63303
## 719 23.801510525 28.84441 39.520604 68.36502
## 720 49.333990670 15.16344 49.733596 64.89704
## 721 50.663627586 27.00120 50.265451 77.26665
## 722 -1.818223565 50.41282 29.272711 79.68553
## 723 16.423462625 44.21537 36.569385 80.78475
## 724 47.255869608 24.23488 48.902348 73.13723
## 725 43.120180976 30.38693 47.248072 77.63501
## 726 48.849958873 23.54251 49.539984 73.08250
## 727 27.417121290 35.38399 40.966849 76.35084
## 728 56.596933573 19.76147 52.638773 72.40024
## 729 22.560676057 34.01056 39.024270 73.03483
## 730 44.169791965 28.65278 47.667917 76.32070
## 731 4.238312989 37.26513 31.695325 68.96045
## 732 -5.199106897 45.65226 27.920357 73.57261
## 733 6.014335400 49.88725 32.405734 82.29298
## 734 -5.393109096 39.21596 27.842756 67.05872
## 735 -0.190447501 34.28567 29.923821 64.20949
## 736 25.824367430 31.61519 40.329747 71.94493
## 737 -5.480912516 45.41860 27.807635 73.22624
## 738 26.768135754 27.13289 40.707254 67.84014
## 739 55.124538760 27.54115 52.049816 79.59097
## 740 41.983816917 18.70567 46.793527 65.49920
## 741 40.430146791 23.83582 46.172059 70.00788
## 742 11.543229646 42.07820 34.617292 76.69550
## 743 23.344603779 39.97884 39.337842 79.31668
## 744 47.801610208 35.62204 49.120644 84.74268
## 745 48.432942538 20.03569 49.373177 69.40887
## 746 6.263462375 38.71452 32.505385 71.21991
## 747 29.852761363 26.80130 41.941105 68.74240
## 748 37.933199403 19.44687 45.173280 64.62014
## 749 7.295352716 40.77252 32.918141 73.69066
## 750 13.801330603 41.12838 35.520532 76.64892
## 751 20.359139182 46.69470 38.143656 84.83836
## 752 20.540781307 41.67626 38.216313 79.89257
## 753 57.186875020 22.71430 52.874750 75.58905
## 754 59.817361340 28.15108 53.926945 82.07802
## 755 -7.717159127 45.32616 26.913136 72.23930
## 756 32.911955819 27.24689 43.164782 70.41167
## 757 42.000486008 34.77465 46.800194 81.57485
## 758 -4.360336715 43.73523 28.255865 71.99110
## 759 -2.042368646 46.00662 29.183053 75.18967
## 760 22.240042503 43.88763 38.896017 82.78365
## 761 0.078375342 43.18015 30.031350 73.21150
## 762 29.185384512 42.66579 41.674154 84.33994
## 763 8.177388182 41.96065 33.270955 75.23161
## 764 45.126663966 14.05734 48.050666 62.10801
## 765 46.540126496 28.13800 48.616051 76.75405
## 766 31.165217231 32.67398 42.466087 75.14006
## 767 58.719370710 13.61270 53.487748 67.10044
## 768 48.729162384 17.39964 49.491665 66.89131
## 769 9.040006869 38.33379 33.616003 71.94979
## 770 49.753134190 28.92910 49.901254 78.83035
## 771 3.110962033 42.41768 31.244385 73.66207
## 772 51.522445448 25.58867 50.608978 76.19765
## 773 46.428897718 29.46489 48.571559 78.03645
## 774 -2.325825333 47.28093 29.069670 76.35060
## 775 53.906231963 21.14608 51.562493 72.70857
## 776 44.187532039 23.18860 47.675013 70.86362
## 777 10.039842247 42.81276 34.015937 76.82870
## 778 30.829978127 34.19066 42.331991 76.52265
## 779 19.890107301 37.37220 37.956043 75.32825
## 780 36.941563801 22.56832 44.776626 67.34494
## 781 14.489336554 29.78114 35.795735 65.57688
## 782 2.418134015 47.06325 30.967254 78.03051
## 783 29.822278421 44.50452 41.928911 86.43343
## 784 43.437362127 21.58854 47.374945 68.96348
## 785 -5.301772824 39.80702 27.879291 67.68631
## 786 5.460497751 42.41535 32.184199 74.59955
## 787 44.912206372 25.33359 47.964883 73.29847
## 788 47.464612501 22.02959 48.985845 71.01543
## 789 20.016756144 25.71249 38.006702 63.71919
## 790 56.285124747 27.69978 52.514050 80.21383
## 791 14.925605822 45.78110 35.970242 81.75134
## 792 20.505292749 40.37591 38.202117 78.57802
## 793 4.947609811 41.33912 31.979044 73.31817
## 794 19.449873378 29.38068 37.779949 67.16063
## 795 47.519067293 28.45025 49.007627 77.45788
## 796 49.352313746 28.38465 49.740925 78.12558
## 797 31.510620592 30.23849 42.604248 72.84274
## 798 1.188903076 45.91098 30.475561 76.38655
## 799 47.207768729 25.63481 48.883107 74.51792
## 800 41.790700310 30.28241 46.716280 76.99869
## 801 20.198292152 43.48737 38.079317 81.56669
## 802 -6.237917040 40.82539 27.504833 68.33022
## 803 17.878792400 25.50192 37.151517 62.65344
## 804 22.747236425 29.17459 39.098895 68.27348
## 805 55.372039734 16.85748 52.148816 69.00629
## 806 25.704138882 34.81373 40.281656 75.09539
## 807 24.835474773 34.89243 39.934190 74.82662
## 808 41.264852770 33.91429 46.505941 80.42023
## 809 49.388248157 21.77489 49.755299 71.53019
## 810 27.528446650 21.78209 41.011379 62.79346
## 811 26.376340049 29.75094 40.550536 70.30148
## 812 51.451111287 31.62855 50.580445 82.20899
## 813 4.010260755 42.70379 31.604104 74.30789
## 814 20.168127171 42.81898 38.067251 80.88623
## 815 28.785664372 25.39251 41.514266 66.90677
## 816 39.646026327 33.27215 45.858411 79.13056
## 817 -1.936236657 56.55699 29.225505 85.78249
## 818 29.393150837 27.07302 41.757260 68.83028
## 819 39.532037980 35.76467 45.812815 81.57748
## 820 -8.399492786 38.29439 26.640203 64.93459
## 821 56.199856601 22.90764 52.479943 75.38758
## 822 51.237123895 30.47954 50.494850 80.97439
## 823 3.292536326 54.61037 31.317015 85.92739
## 824 23.048459394 29.97990 39.219384 69.19929
## 825 -1.594924587 53.59131 29.362030 82.95334
## 826 39.015396284 36.45239 45.606159 82.05855
## 827 21.742119323 33.41818 38.696848 72.11503
## 828 58.457655944 14.38088 53.383062 67.76395
## 829 11.036096776 36.15162 34.414439 70.56606
## 830 7.677470632 41.50243 33.070988 74.57342
## 831 12.537970925 36.28324 35.015188 71.29843
## 832 45.791800881 33.18556 48.316720 81.50228
## 833 31.274811842 23.81431 42.509925 66.32424
## 834 -4.810828967 40.59460 28.075668 68.67026
## 835 -4.870159186 44.77749 28.051936 72.82943
## 836 17.353010948 25.70247 36.941204 62.64367
## 837 28.143752753 33.85536 41.257501 75.11286
## 838 6.578480974 35.38117 32.631392 68.01256
## 839 1.419335264 34.08433 30.567734 64.65206
## 840 22.711663784 38.32220 39.084666 77.40687
## 841 19.166167101 38.37906 37.666467 76.04553
## 842 8.774300378 30.08778 33.509720 63.59750
## 843 16.543802505 35.99184 36.617521 72.60936
## 844 42.225335625 24.07780 46.890134 70.96793
## 845 44.247586955 33.11273 47.699035 80.81177
## 846 37.243342733 29.77099 44.897337 74.66832
## 847 -2.522874991 46.90953 28.990850 75.90038
## 848 9.202862841 42.22814 33.681145 75.90929
## 849 21.483835594 34.64702 38.593534 73.24055
## 850 35.070311704 30.74158 44.028125 74.76971
## 851 26.998093699 31.05159 40.799237 71.85083
## 852 4.559644365 37.19127 31.823858 69.01513
## 853 24.361840377 33.53377 39.744736 73.27851
## 854 23.952250781 27.32630 39.580900 66.90720
## 855 22.555263736 35.71174 39.022105 74.73385
## 856 51.876789434 27.74447 50.750716 78.49519
## 857 49.164543126 21.98091 49.665817 71.64672
## 858 -4.517888797 57.59268 28.192844 85.78553
## 859 53.130177010 24.58548 51.252071 75.83755
## 860 42.945878231 24.71737 47.178351 71.89573
## 861 29.796112238 25.15077 41.918445 67.06921
## 862 58.812179519 13.29216 53.524872 66.81703
## 863 32.539413699 32.01752 43.015765 75.03329
## 864 4.324674252 39.73079 31.729870 71.46066
## 865 15.610495193 30.10028 36.244198 66.34447
## 866 4.251844753 54.49601 31.700738 86.19674
## 867 -8.835178108 43.58610 26.465929 70.05202
## 868 31.626613871 39.93293 42.650646 82.58358
## 869 47.929627949 26.36069 49.171851 75.53254
## 870 49.962843254 31.71048 49.985137 81.69562
## 871 34.542141238 29.05739 43.816856 72.87425
## 872 31.121901569 32.08879 42.448761 74.53755
## 873 51.673862729 23.51561 50.669545 74.18516
## 874 8.099576111 45.13238 33.239830 78.37221
## 875 52.620519476 25.55459 51.048208 76.60279
## 876 1.283623918 47.59319 30.513450 78.10664
## 877 14.015075723 30.98529 35.606030 66.59132
## 878 13.836401831 47.35237 35.534561 82.88693
## 879 25.070618999 37.79252 40.028248 77.82076
## 880 4.755247042 44.74703 31.902099 76.64913
## 881 7.218235908 35.48252 32.887294 68.36981
## 882 -3.530001687 45.43351 28.587999 74.02151
## 883 22.191097673 29.46989 38.876439 68.34633
## 884 26.650965163 39.47770 40.660386 80.13808
## 885 0.297888799 36.21062 30.119156 66.32978
## 886 14.788766678 50.16683 35.915507 86.08234
## 887 50.078875893 18.27409 50.031550 68.30565
## 888 48.587831911 21.07189 49.435133 70.50702
## 889 -6.595486852 41.54832 27.361805 68.91012
## 890 12.415291853 43.75387 34.966117 78.71998
## 891 34.298637498 31.98895 43.719455 75.70841
## 892 -0.275156084 54.05384 29.889938 83.94378
## 893 1.536679855 44.12599 30.614672 74.74067
## 894 37.246204410 22.09232 44.898482 66.99080
## 895 50.340816258 13.12098 50.136327 63.25731
## 896 3.530969843 45.72760 31.412388 77.13999
## 897 -4.581355567 45.70641 28.167458 73.87386
## 898 34.288542215 37.40438 43.715417 81.11979
## 899 20.216350139 36.34726 38.086540 74.43380
## 900 30.833109359 34.30278 42.333244 76.63602
## 901 44.413334690 14.08231 47.765334 61.84764
## 902 41.467110012 37.35504 46.586844 83.94188
## 903 28.812145728 24.76617 41.524858 66.29103
## 904 -5.968423348 51.53830 27.612631 79.15093
## 905 16.997654978 34.78716 36.799062 71.58622
## 906 51.386943648 31.38690 50.554777 81.94167
## 907 21.271848832 43.58203 38.508740 82.09077
## 908 43.176320344 17.50175 47.270528 64.77228
## 909 18.939912471 21.74969 37.575965 59.32565
## 910 40.677542593 21.43413 46.271017 67.70515
## 911 0.115846097 47.76271 30.046338 77.80905
## 912 46.448879195 24.58812 48.579552 73.16767
## 913 40.043594786 27.90682 46.017438 73.92426
## 914 10.962558812 40.95274 34.385024 75.33777
## 915 -6.788334555 40.62554 27.284666 67.91020
## 916 52.561174328 21.63344 51.024470 72.65791
## 917 59.872334201 17.72712 53.948934 71.67605
## 918 23.752204676 24.21693 39.500882 63.71781
## 919 0.884615812 42.59021 30.353846 72.94405
## 920 13.874710409 39.65640 35.549884 75.20629
## 921 40.970236841 22.82050 46.388095 69.20859
## 922 59.714630400 25.69223 53.885852 79.57808
## 923 13.033175785 35.63409 35.213270 70.84736
## 924 53.806639034 23.95460 51.522656 75.47726
## 925 7.892646305 43.66273 33.157059 76.81979
## 926 45.283657918 25.85104 48.113463 73.96450
## 927 6.384794959 43.90833 32.553918 76.46225
## 928 10.559404963 29.94043 34.223762 64.16420
## 929 38.918110831 23.30530 45.567244 68.87255
## 930 28.500437071 37.61805 41.400175 79.01822
## 931 8.912190818 53.14492 33.564876 86.70979
## 932 50.665318943 28.71903 50.266128 78.98516
## 933 3.756918737 47.20367 31.502767 78.70644
## 934 -1.198237271 40.71026 29.520705 70.23096
## 935 59.425098873 20.02778 53.770040 73.79782
## 936 22.673792730 35.33238 39.069517 74.40190
## 937 25.674071363 30.53549 40.269629 70.80512
## 938 9.142799091 46.50961 33.657120 80.16673
## 939 -2.346206799 44.84217 29.061517 73.90368
## 940 2.062083972 44.89179 30.824834 75.71662
## 941 4.533684549 40.93883 31.813474 72.75230
## 942 21.365852051 43.04796 38.546341 81.59430
## 943 50.216303042 18.38068 50.086521 68.46720
## 944 28.756729313 32.40840 41.502692 73.91109
## 945 24.397745451 38.24761 39.759098 78.00671
## 946 10.058995502 45.53364 34.023598 79.55723
## 947 2.503838919 45.74299 31.001536 76.74453
## 948 5.375193765 48.35207 32.150078 80.50215
## 949 -4.866806804 53.33632 28.053277 81.38960
## 950 14.590581348 39.78180 35.836233 75.61803
## 951 4.388284951 41.74764 31.755314 73.50295
## 952 5.934556942 41.72808 32.373823 74.10190
## 953 57.283392961 21.21697 52.913357 74.13033
## 954 58.921540072 18.11306 53.568616 71.68168
## 955 13.945402424 44.09885 35.578161 79.67702
## 956 56.349351874 21.13375 52.539741 73.67349
## 957 0.637215364 43.38039 30.254886 73.63527
## 958 18.978624200 29.13427 37.591450 66.72572
## 959 34.495270152 35.59658 43.798108 79.39469
## 960 6.579339593 39.89921 32.631736 72.53094
## 961 2.116218146 40.66167 30.846487 71.50816
## 962 4.264002484 49.66727 31.705601 81.37287
## 963 13.643642447 34.93970 35.457457 70.39715
## 964 39.417175516 29.55686 45.766870 75.32373
## 965 -4.877937492 56.27135 28.048825 84.32018
## 966 -8.562474661 57.73874 26.575010 84.31375
## 967 23.036260721 35.22678 39.214504 74.44129
## 968 53.139597094 15.67816 51.255839 66.93400
## 969 0.987494527 43.71381 30.394998 74.10880
## 970 36.827654256 31.73686 44.731062 76.46792
## 971 48.509411153 28.47629 49.403764 77.88006
## 972 6.347061363 37.02568 32.538825 69.56450
## 973 16.418235581 32.08203 36.567294 68.64932
## 974 48.419392994 22.86978 49.367757 72.23753
## 975 27.906343085 33.20243 41.162537 74.36497
## 976 31.445277792 26.67261 42.578111 69.25072
## 977 2.424089080 40.71181 30.969636 71.68145
## 978 0.344847227 54.13075 30.137939 84.26869
## 979 56.424861164 27.72447 52.569944 80.29441
## 980 51.982359935 29.85014 50.792944 80.64308
## 981 23.093353189 26.82187 39.237341 66.05921
## 982 58.942317762 24.00361 53.576927 77.58054
## 983 10.974134668 39.28474 34.389654 73.67439
## 984 48.930612574 24.37925 49.572245 73.95150
## 985 8.577752914 42.73926 33.431101 76.17036
## 986 52.921400380 24.71438 51.168560 75.88294
## 987 33.836552929 45.08373 43.534621 88.61836
## 988 4.497750383 41.58869 31.799100 73.38779
## 989 5.353448470 39.82160 32.141379 71.96298
## 990 -1.049586062 45.27588 29.580166 74.85605
## 991 21.283038780 40.29893 38.513216 78.81214
## 992 52.584001136 17.78124 51.033600 68.81484
## 993 14.571139372 32.59373 35.828456 68.42218
## 994 46.116651581 28.52591 48.446661 76.97257
## 995 30.967467551 35.01519 42.386987 77.40218
## 996 29.648423810 32.75105 41.859370 74.61041
## 997 38.845490371 30.35911 45.538196 75.89731
## 998 43.836238561 15.00811 47.534495 62.54261
## 999 14.683130528 43.16221 35.873252 79.03546
## 1000 1.491731950 47.18072 30.596693 77.77741
## above_cutoff below_cutoff
## 1 FALSE TRUE
## 2 FALSE TRUE
## 3 FALSE TRUE
## 4 FALSE TRUE
## 5 FALSE TRUE
## 6 FALSE TRUE
## 7 TRUE FALSE
## 8 FALSE TRUE
## 9 FALSE TRUE
## 10 FALSE TRUE
## 11 FALSE TRUE
## 12 TRUE FALSE
## 13 FALSE TRUE
## 14 FALSE TRUE
## 15 FALSE TRUE
## 16 FALSE TRUE
## 17 FALSE TRUE
## 18 FALSE TRUE
## 19 FALSE TRUE
## 20 FALSE TRUE
## 21 FALSE TRUE
## 22 TRUE FALSE
## 23 TRUE FALSE
## 24 FALSE TRUE
## 25 FALSE TRUE
## 26 FALSE TRUE
## 27 TRUE FALSE
## 28 FALSE TRUE
## 29 FALSE TRUE
## 30 FALSE TRUE
## 31 FALSE TRUE
## 32 FALSE TRUE
## 33 FALSE TRUE
## 34 FALSE TRUE
## 35 FALSE TRUE
## 36 TRUE FALSE
## 37 FALSE TRUE
## 38 FALSE TRUE
## 39 FALSE TRUE
## 40 FALSE TRUE
## 41 FALSE TRUE
## 42 FALSE TRUE
## 43 FALSE TRUE
## 44 FALSE TRUE
## 45 FALSE TRUE
## 46 FALSE TRUE
## 47 FALSE TRUE
## 48 FALSE TRUE
## 49 TRUE FALSE
## 50 FALSE TRUE
## 51 FALSE TRUE
## 52 FALSE TRUE
## 53 TRUE FALSE
## 54 FALSE TRUE
## 55 FALSE TRUE
## 56 FALSE TRUE
## 57 FALSE TRUE
## 58 TRUE FALSE
## 59 FALSE TRUE
## 60 FALSE TRUE
## 61 FALSE TRUE
## 62 FALSE TRUE
## 63 FALSE TRUE
## 64 FALSE TRUE
## 65 FALSE TRUE
## 66 FALSE TRUE
## 67 FALSE TRUE
## 68 FALSE TRUE
## 69 FALSE TRUE
## 70 FALSE TRUE
## 71 TRUE FALSE
## 72 TRUE FALSE
## 73 FALSE TRUE
## 74 FALSE TRUE
## 75 FALSE TRUE
## 76 FALSE TRUE
## 77 TRUE FALSE
## 78 FALSE TRUE
## 79 FALSE TRUE
## 80 FALSE TRUE
## 81 FALSE TRUE
## 82 FALSE TRUE
## 83 FALSE TRUE
## 84 TRUE FALSE
## 85 FALSE TRUE
## 86 FALSE TRUE
## 87 FALSE TRUE
## 88 FALSE TRUE
## 89 FALSE TRUE
## 90 FALSE TRUE
## 91 FALSE TRUE
## 92 FALSE TRUE
## 93 FALSE TRUE
## 94 FALSE TRUE
## 95 FALSE TRUE
## 96 FALSE TRUE
## 97 FALSE TRUE
## 98 FALSE TRUE
## 99 TRUE FALSE
## 100 TRUE FALSE
## 101 FALSE TRUE
## 102 FALSE TRUE
## 103 FALSE TRUE
## 104 FALSE TRUE
## 105 FALSE TRUE
## 106 FALSE TRUE
## 107 FALSE TRUE
## 108 FALSE TRUE
## 109 FALSE TRUE
## 110 FALSE TRUE
## 111 FALSE TRUE
## 112 FALSE TRUE
## 113 TRUE FALSE
## 114 FALSE TRUE
## 115 TRUE FALSE
## 116 FALSE TRUE
## 117 FALSE TRUE
## 118 FALSE TRUE
## 119 FALSE TRUE
## 120 FALSE TRUE
## 121 FALSE TRUE
## 122 TRUE FALSE
## 123 FALSE TRUE
## 124 FALSE TRUE
## 125 FALSE TRUE
## 126 FALSE TRUE
## 127 FALSE TRUE
## 128 FALSE TRUE
## 129 FALSE TRUE
## 130 FALSE TRUE
## 131 FALSE TRUE
## 132 FALSE TRUE
## 133 TRUE FALSE
## 134 FALSE TRUE
## 135 FALSE TRUE
## 136 FALSE TRUE
## 137 FALSE TRUE
## 138 TRUE FALSE
## 139 FALSE TRUE
## 140 FALSE TRUE
## 141 TRUE FALSE
## 142 FALSE TRUE
## 143 FALSE TRUE
## 144 FALSE TRUE
## 145 FALSE TRUE
## 146 FALSE TRUE
## 147 FALSE TRUE
## 148 FALSE TRUE
## 149 FALSE TRUE
## 150 FALSE TRUE
## 151 FALSE TRUE
## 152 FALSE TRUE
## 153 FALSE TRUE
## 154 FALSE TRUE
## 155 FALSE TRUE
## 156 FALSE TRUE
## 157 FALSE TRUE
## 158 TRUE FALSE
## 159 FALSE TRUE
## 160 FALSE TRUE
## 161 TRUE FALSE
## 162 FALSE TRUE
## 163 TRUE FALSE
## 164 FALSE TRUE
## 165 FALSE TRUE
## 166 FALSE TRUE
## 167 FALSE TRUE
## 168 TRUE FALSE
## 169 FALSE TRUE
## 170 FALSE TRUE
## 171 FALSE TRUE
## 172 FALSE TRUE
## 173 FALSE TRUE
## 174 TRUE FALSE
## 175 FALSE TRUE
## 176 TRUE FALSE
## 177 FALSE TRUE
## 178 FALSE TRUE
## 179 FALSE TRUE
## 180 FALSE TRUE
## 181 FALSE TRUE
## 182 FALSE TRUE
## 183 FALSE TRUE
## 184 TRUE FALSE
## 185 FALSE TRUE
## 186 FALSE TRUE
## 187 TRUE FALSE
## 188 FALSE TRUE
## 189 FALSE TRUE
## 190 FALSE TRUE
## 191 TRUE FALSE
## 192 TRUE FALSE
## 193 FALSE TRUE
## 194 FALSE TRUE
## 195 FALSE TRUE
## 196 TRUE FALSE
## 197 FALSE TRUE
## 198 TRUE FALSE
## 199 FALSE TRUE
## 200 FALSE TRUE
## 201 FALSE TRUE
## 202 TRUE FALSE
## 203 FALSE TRUE
## 204 FALSE TRUE
## 205 FALSE TRUE
## 206 FALSE TRUE
## 207 FALSE TRUE
## 208 FALSE TRUE
## 209 TRUE FALSE
## 210 FALSE TRUE
## 211 FALSE TRUE
## 212 FALSE TRUE
## 213 FALSE TRUE
## 214 FALSE TRUE
## 215 FALSE TRUE
## 216 FALSE TRUE
## 217 FALSE TRUE
## 218 FALSE TRUE
## 219 FALSE TRUE
## 220 TRUE FALSE
## 221 FALSE TRUE
## 222 FALSE TRUE
## 223 TRUE FALSE
## 224 FALSE TRUE
## 225 FALSE TRUE
## 226 FALSE TRUE
## 227 FALSE TRUE
## 228 FALSE TRUE
## 229 FALSE TRUE
## 230 FALSE TRUE
## 231 TRUE FALSE
## 232 FALSE TRUE
## 233 FALSE TRUE
## 234 FALSE TRUE
## 235 FALSE TRUE
## 236 FALSE TRUE
## 237 FALSE TRUE
## 238 FALSE TRUE
## 239 FALSE TRUE
## 240 FALSE TRUE
## 241 TRUE FALSE
## 242 TRUE FALSE
## 243 FALSE TRUE
## 244 FALSE TRUE
## 245 FALSE TRUE
## 246 FALSE TRUE
## 247 FALSE TRUE
## 248 TRUE FALSE
## 249 FALSE TRUE
## 250 FALSE TRUE
## 251 FALSE TRUE
## 252 FALSE TRUE
## 253 FALSE TRUE
## 254 FALSE TRUE
## 255 FALSE TRUE
## 256 FALSE TRUE
## 257 FALSE TRUE
## 258 FALSE TRUE
## 259 FALSE TRUE
## 260 TRUE FALSE
## 261 FALSE TRUE
## 262 FALSE TRUE
## 263 TRUE FALSE
## 264 FALSE TRUE
## 265 FALSE TRUE
## 266 FALSE TRUE
## 267 FALSE TRUE
## 268 FALSE TRUE
## 269 FALSE TRUE
## 270 FALSE TRUE
## 271 TRUE FALSE
## 272 FALSE TRUE
## 273 FALSE TRUE
## 274 FALSE TRUE
## 275 FALSE TRUE
## 276 FALSE TRUE
## 277 FALSE TRUE
## 278 FALSE TRUE
## 279 FALSE TRUE
## 280 FALSE TRUE
## 281 FALSE TRUE
## 282 FALSE TRUE
## 283 FALSE TRUE
## 284 FALSE TRUE
## 285 FALSE TRUE
## 286 FALSE TRUE
## 287 TRUE FALSE
## 288 FALSE TRUE
## 289 FALSE TRUE
## 290 FALSE TRUE
## 291 TRUE FALSE
## 292 TRUE FALSE
## 293 FALSE TRUE
## 294 TRUE FALSE
## 295 TRUE FALSE
## 296 FALSE TRUE
## 297 TRUE FALSE
## 298 FALSE TRUE
## 299 FALSE TRUE
## 300 FALSE TRUE
## 301 FALSE TRUE
## 302 FALSE TRUE
## 303 FALSE TRUE
## 304 TRUE FALSE
## 305 FALSE TRUE
## 306 FALSE TRUE
## 307 FALSE TRUE
## 308 TRUE FALSE
## 309 FALSE TRUE
## 310 TRUE FALSE
## 311 FALSE TRUE
## 312 TRUE FALSE
## 313 FALSE TRUE
## 314 FALSE TRUE
## 315 FALSE TRUE
## 316 FALSE TRUE
## 317 FALSE TRUE
## 318 FALSE TRUE
## 319 FALSE TRUE
## 320 TRUE FALSE
## 321 FALSE TRUE
## 322 FALSE TRUE
## 323 FALSE TRUE
## 324 FALSE TRUE
## 325 FALSE TRUE
## 326 FALSE TRUE
## 327 FALSE TRUE
## 328 FALSE TRUE
## 329 FALSE TRUE
## 330 FALSE TRUE
## 331 FALSE TRUE
## 332 FALSE TRUE
## 333 FALSE TRUE
## 334 FALSE TRUE
## 335 FALSE TRUE
## 336 FALSE TRUE
## 337 FALSE TRUE
## 338 FALSE TRUE
## 339 FALSE TRUE
## 340 FALSE TRUE
## 341 FALSE TRUE
## 342 FALSE TRUE
## 343 FALSE TRUE
## 344 FALSE TRUE
## 345 FALSE TRUE
## 346 TRUE FALSE
## 347 FALSE TRUE
## 348 FALSE TRUE
## 349 FALSE TRUE
## 350 FALSE TRUE
## 351 FALSE TRUE
## 352 FALSE TRUE
## 353 FALSE TRUE
## 354 FALSE TRUE
## 355 FALSE TRUE
## 356 FALSE TRUE
## 357 FALSE TRUE
## 358 FALSE TRUE
## 359 FALSE TRUE
## 360 FALSE TRUE
## 361 FALSE TRUE
## 362 FALSE TRUE
## 363 FALSE TRUE
## 364 FALSE TRUE
## 365 FALSE TRUE
## 366 FALSE TRUE
## 367 FALSE TRUE
## 368 FALSE TRUE
## 369 FALSE TRUE
## 370 FALSE TRUE
## 371 TRUE FALSE
## 372 FALSE TRUE
## 373 FALSE TRUE
## 374 FALSE TRUE
## 375 TRUE FALSE
## 376 FALSE TRUE
## 377 FALSE TRUE
## 378 FALSE TRUE
## 379 FALSE TRUE
## 380 FALSE TRUE
## 381 FALSE TRUE
## 382 FALSE TRUE
## 383 FALSE TRUE
## 384 FALSE TRUE
## 385 FALSE TRUE
## 386 FALSE TRUE
## 387 TRUE FALSE
## 388 FALSE TRUE
## 389 FALSE TRUE
## 390 FALSE TRUE
## 391 FALSE TRUE
## 392 FALSE TRUE
## 393 FALSE TRUE
## 394 FALSE TRUE
## 395 FALSE TRUE
## 396 TRUE FALSE
## 397 FALSE TRUE
## 398 FALSE TRUE
## 399 FALSE TRUE
## 400 FALSE TRUE
## 401 FALSE TRUE
## 402 TRUE FALSE
## 403 TRUE FALSE
## 404 TRUE FALSE
## 405 FALSE TRUE
## 406 FALSE TRUE
## 407 FALSE TRUE
## 408 FALSE TRUE
## 409 FALSE TRUE
## 410 FALSE TRUE
## 411 FALSE TRUE
## 412 FALSE TRUE
## 413 FALSE TRUE
## 414 FALSE TRUE
## 415 FALSE TRUE
## 416 FALSE TRUE
## 417 FALSE TRUE
## 418 FALSE TRUE
## 419 FALSE TRUE
## 420 FALSE TRUE
## 421 FALSE TRUE
## 422 TRUE FALSE
## 423 FALSE TRUE
## 424 TRUE FALSE
## 425 FALSE TRUE
## 426 FALSE TRUE
## 427 FALSE TRUE
## 428 FALSE TRUE
## 429 FALSE TRUE
## 430 FALSE TRUE
## 431 TRUE FALSE
## 432 TRUE FALSE
## 433 TRUE FALSE
## 434 FALSE TRUE
## 435 FALSE TRUE
## 436 FALSE TRUE
## 437 FALSE TRUE
## 438 TRUE FALSE
## 439 FALSE TRUE
## 440 TRUE FALSE
## 441 FALSE TRUE
## 442 FALSE TRUE
## 443 FALSE TRUE
## 444 FALSE TRUE
## 445 FALSE TRUE
## 446 FALSE TRUE
## 447 FALSE TRUE
## 448 FALSE TRUE
## 449 FALSE TRUE
## 450 TRUE FALSE
## 451 FALSE TRUE
## 452 FALSE TRUE
## 453 FALSE TRUE
## 454 FALSE TRUE
## 455 FALSE TRUE
## 456 TRUE FALSE
## 457 FALSE TRUE
## 458 TRUE FALSE
## 459 FALSE TRUE
## 460 FALSE TRUE
## 461 FALSE TRUE
## 462 FALSE TRUE
## 463 TRUE FALSE
## 464 FALSE TRUE
## 465 FALSE TRUE
## 466 FALSE TRUE
## 467 FALSE TRUE
## 468 FALSE TRUE
## 469 FALSE TRUE
## 470 FALSE TRUE
## 471 FALSE TRUE
## 472 FALSE TRUE
## 473 TRUE FALSE
## 474 FALSE TRUE
## 475 FALSE TRUE
## 476 FALSE TRUE
## 477 FALSE TRUE
## 478 FALSE TRUE
## 479 FALSE TRUE
## 480 FALSE TRUE
## 481 FALSE TRUE
## 482 TRUE FALSE
## 483 FALSE TRUE
## 484 FALSE TRUE
## 485 TRUE FALSE
## 486 TRUE FALSE
## 487 FALSE TRUE
## 488 FALSE TRUE
## 489 FALSE TRUE
## 490 FALSE TRUE
## 491 FALSE TRUE
## 492 FALSE TRUE
## 493 TRUE FALSE
## 494 TRUE FALSE
## 495 FALSE TRUE
## 496 TRUE FALSE
## 497 FALSE TRUE
## 498 FALSE TRUE
## 499 TRUE FALSE
## 500 FALSE TRUE
## 501 TRUE FALSE
## 502 TRUE FALSE
## 503 TRUE FALSE
## 504 TRUE FALSE
## 505 TRUE FALSE
## 506 TRUE FALSE
## 507 TRUE FALSE
## 508 FALSE TRUE
## 509 TRUE FALSE
## 510 TRUE FALSE
## 511 TRUE FALSE
## 512 TRUE FALSE
## 513 TRUE FALSE
## 514 FALSE TRUE
## 515 TRUE FALSE
## 516 TRUE FALSE
## 517 TRUE FALSE
## 518 FALSE TRUE
## 519 FALSE TRUE
## 520 TRUE FALSE
## 521 TRUE FALSE
## 522 TRUE FALSE
## 523 TRUE FALSE
## 524 TRUE FALSE
## 525 TRUE FALSE
## 526 TRUE FALSE
## 527 TRUE FALSE
## 528 FALSE TRUE
## 529 TRUE FALSE
## 530 TRUE FALSE
## 531 TRUE FALSE
## 532 TRUE FALSE
## 533 TRUE FALSE
## 534 TRUE FALSE
## 535 FALSE TRUE
## 536 TRUE FALSE
## 537 TRUE FALSE
## 538 TRUE FALSE
## 539 TRUE FALSE
## 540 TRUE FALSE
## 541 TRUE FALSE
## 542 TRUE FALSE
## 543 TRUE FALSE
## 544 TRUE FALSE
## 545 TRUE FALSE
## 546 FALSE TRUE
## 547 TRUE FALSE
## 548 TRUE FALSE
## 549 TRUE FALSE
## 550 TRUE FALSE
## 551 FALSE TRUE
## 552 TRUE FALSE
## 553 FALSE TRUE
## 554 TRUE FALSE
## 555 TRUE FALSE
## 556 TRUE FALSE
## 557 TRUE FALSE
## 558 FALSE TRUE
## 559 TRUE FALSE
## 560 FALSE TRUE
## 561 TRUE FALSE
## 562 TRUE FALSE
## 563 TRUE FALSE
## 564 TRUE FALSE
## 565 TRUE FALSE
## 566 TRUE FALSE
## 567 TRUE FALSE
## 568 TRUE FALSE
## 569 TRUE FALSE
## 570 TRUE FALSE
## 571 TRUE FALSE
## 572 TRUE FALSE
## 573 TRUE FALSE
## 574 TRUE FALSE
## 575 TRUE FALSE
## 576 FALSE TRUE
## 577 TRUE FALSE
## 578 TRUE FALSE
## 579 TRUE FALSE
## 580 TRUE FALSE
## 581 TRUE FALSE
## 582 TRUE FALSE
## 583 TRUE FALSE
## 584 TRUE FALSE
## 585 TRUE FALSE
## 586 TRUE FALSE
## 587 TRUE FALSE
## 588 FALSE TRUE
## 589 TRUE FALSE
## 590 TRUE FALSE
## 591 TRUE FALSE
## 592 TRUE FALSE
## 593 TRUE FALSE
## 594 TRUE FALSE
## 595 TRUE FALSE
## 596 TRUE FALSE
## 597 FALSE TRUE
## 598 TRUE FALSE
## 599 TRUE FALSE
## 600 TRUE FALSE
## 601 TRUE FALSE
## 602 TRUE FALSE
## 603 TRUE FALSE
## 604 FALSE TRUE
## 605 TRUE FALSE
## 606 TRUE FALSE
## 607 TRUE FALSE
## 608 TRUE FALSE
## 609 TRUE FALSE
## 610 TRUE FALSE
## 611 TRUE FALSE
## 612 TRUE FALSE
## 613 TRUE FALSE
## 614 TRUE FALSE
## 615 TRUE FALSE
## 616 TRUE FALSE
## 617 FALSE TRUE
## 618 TRUE FALSE
## 619 TRUE FALSE
## 620 TRUE FALSE
## 621 TRUE FALSE
## 622 TRUE FALSE
## 623 FALSE TRUE
## 624 TRUE FALSE
## 625 TRUE FALSE
## 626 FALSE TRUE
## 627 TRUE FALSE
## 628 TRUE FALSE
## 629 TRUE FALSE
## 630 FALSE TRUE
## 631 TRUE FALSE
## 632 TRUE FALSE
## 633 TRUE FALSE
## 634 TRUE FALSE
## 635 TRUE FALSE
## 636 TRUE FALSE
## 637 TRUE FALSE
## 638 TRUE FALSE
## 639 TRUE FALSE
## 640 FALSE TRUE
## 641 TRUE FALSE
## 642 TRUE FALSE
## 643 TRUE FALSE
## 644 TRUE FALSE
## 645 TRUE FALSE
## 646 TRUE FALSE
## 647 TRUE FALSE
## 648 TRUE FALSE
## 649 FALSE TRUE
## 650 FALSE TRUE
## 651 TRUE FALSE
## 652 TRUE FALSE
## 653 TRUE FALSE
## 654 TRUE FALSE
## 655 TRUE FALSE
## 656 TRUE FALSE
## 657 TRUE FALSE
## 658 TRUE FALSE
## 659 TRUE FALSE
## 660 TRUE FALSE
## 661 TRUE FALSE
## 662 TRUE FALSE
## 663 TRUE FALSE
## 664 TRUE FALSE
## 665 FALSE TRUE
## 666 TRUE FALSE
## 667 TRUE FALSE
## 668 TRUE FALSE
## 669 TRUE FALSE
## 670 TRUE FALSE
## 671 TRUE FALSE
## 672 TRUE FALSE
## 673 TRUE FALSE
## 674 TRUE FALSE
## 675 TRUE FALSE
## 676 FALSE TRUE
## 677 TRUE FALSE
## 678 TRUE FALSE
## 679 TRUE FALSE
## 680 TRUE FALSE
## 681 FALSE TRUE
## 682 TRUE FALSE
## 683 TRUE FALSE
## 684 TRUE FALSE
## 685 FALSE TRUE
## 686 TRUE FALSE
## 687 FALSE TRUE
## 688 TRUE FALSE
## 689 TRUE FALSE
## 690 TRUE FALSE
## 691 TRUE FALSE
## 692 TRUE FALSE
## 693 TRUE FALSE
## 694 FALSE TRUE
## 695 TRUE FALSE
## 696 TRUE FALSE
## 697 FALSE TRUE
## 698 TRUE FALSE
## 699 TRUE FALSE
## 700 TRUE FALSE
## 701 TRUE FALSE
## 702 TRUE FALSE
## 703 FALSE TRUE
## 704 TRUE FALSE
## 705 TRUE FALSE
## 706 TRUE FALSE
## 707 TRUE FALSE
## 708 TRUE FALSE
## 709 FALSE TRUE
## 710 TRUE FALSE
## 711 TRUE FALSE
## 712 TRUE FALSE
## 713 TRUE FALSE
## 714 TRUE FALSE
## 715 TRUE FALSE
## 716 FALSE TRUE
## 717 TRUE FALSE
## 718 TRUE FALSE
## 719 TRUE FALSE
## 720 TRUE FALSE
## 721 TRUE FALSE
## 722 FALSE TRUE
## 723 TRUE FALSE
## 724 TRUE FALSE
## 725 TRUE FALSE
## 726 TRUE FALSE
## 727 TRUE FALSE
## 728 TRUE FALSE
## 729 TRUE FALSE
## 730 TRUE FALSE
## 731 TRUE FALSE
## 732 FALSE TRUE
## 733 TRUE FALSE
## 734 FALSE TRUE
## 735 FALSE TRUE
## 736 TRUE FALSE
## 737 FALSE TRUE
## 738 TRUE FALSE
## 739 TRUE FALSE
## 740 TRUE FALSE
## 741 TRUE FALSE
## 742 TRUE FALSE
## 743 TRUE FALSE
## 744 TRUE FALSE
## 745 TRUE FALSE
## 746 TRUE FALSE
## 747 TRUE FALSE
## 748 TRUE FALSE
## 749 TRUE FALSE
## 750 TRUE FALSE
## 751 TRUE FALSE
## 752 TRUE FALSE
## 753 TRUE FALSE
## 754 TRUE FALSE
## 755 FALSE TRUE
## 756 TRUE FALSE
## 757 TRUE FALSE
## 758 FALSE TRUE
## 759 FALSE TRUE
## 760 TRUE FALSE
## 761 TRUE FALSE
## 762 TRUE FALSE
## 763 TRUE FALSE
## 764 TRUE FALSE
## 765 TRUE FALSE
## 766 TRUE FALSE
## 767 TRUE FALSE
## 768 TRUE FALSE
## 769 TRUE FALSE
## 770 TRUE FALSE
## 771 TRUE FALSE
## 772 TRUE FALSE
## 773 TRUE FALSE
## 774 FALSE TRUE
## 775 TRUE FALSE
## 776 TRUE FALSE
## 777 TRUE FALSE
## 778 TRUE FALSE
## 779 TRUE FALSE
## 780 TRUE FALSE
## 781 TRUE FALSE
## 782 TRUE FALSE
## 783 TRUE FALSE
## 784 TRUE FALSE
## 785 FALSE TRUE
## 786 TRUE FALSE
## 787 TRUE FALSE
## 788 TRUE FALSE
## 789 TRUE FALSE
## 790 TRUE FALSE
## 791 TRUE FALSE
## 792 TRUE FALSE
## 793 TRUE FALSE
## 794 TRUE FALSE
## 795 TRUE FALSE
## 796 TRUE FALSE
## 797 TRUE FALSE
## 798 TRUE FALSE
## 799 TRUE FALSE
## 800 TRUE FALSE
## 801 TRUE FALSE
## 802 FALSE TRUE
## 803 TRUE FALSE
## 804 TRUE FALSE
## 805 TRUE FALSE
## 806 TRUE FALSE
## 807 TRUE FALSE
## 808 TRUE FALSE
## 809 TRUE FALSE
## 810 TRUE FALSE
## 811 TRUE FALSE
## 812 TRUE FALSE
## 813 TRUE FALSE
## 814 TRUE FALSE
## 815 TRUE FALSE
## 816 TRUE FALSE
## 817 FALSE TRUE
## 818 TRUE FALSE
## 819 TRUE FALSE
## 820 FALSE TRUE
## 821 TRUE FALSE
## 822 TRUE FALSE
## 823 TRUE FALSE
## 824 TRUE FALSE
## 825 FALSE TRUE
## 826 TRUE FALSE
## 827 TRUE FALSE
## 828 TRUE FALSE
## 829 TRUE FALSE
## 830 TRUE FALSE
## 831 TRUE FALSE
## 832 TRUE FALSE
## 833 TRUE FALSE
## 834 FALSE TRUE
## 835 FALSE TRUE
## 836 TRUE FALSE
## 837 TRUE FALSE
## 838 TRUE FALSE
## 839 TRUE FALSE
## 840 TRUE FALSE
## 841 TRUE FALSE
## 842 TRUE FALSE
## 843 TRUE FALSE
## 844 TRUE FALSE
## 845 TRUE FALSE
## 846 TRUE FALSE
## 847 FALSE TRUE
## 848 TRUE FALSE
## 849 TRUE FALSE
## 850 TRUE FALSE
## 851 TRUE FALSE
## 852 TRUE FALSE
## 853 TRUE FALSE
## 854 TRUE FALSE
## 855 TRUE FALSE
## 856 TRUE FALSE
## 857 TRUE FALSE
## 858 FALSE TRUE
## 859 TRUE FALSE
## 860 TRUE FALSE
## 861 TRUE FALSE
## 862 TRUE FALSE
## 863 TRUE FALSE
## 864 TRUE FALSE
## 865 TRUE FALSE
## 866 TRUE FALSE
## 867 FALSE TRUE
## 868 TRUE FALSE
## 869 TRUE FALSE
## 870 TRUE FALSE
## 871 TRUE FALSE
## 872 TRUE FALSE
## 873 TRUE FALSE
## 874 TRUE FALSE
## 875 TRUE FALSE
## 876 TRUE FALSE
## 877 TRUE FALSE
## 878 TRUE FALSE
## 879 TRUE FALSE
## 880 TRUE FALSE
## 881 TRUE FALSE
## 882 FALSE TRUE
## 883 TRUE FALSE
## 884 TRUE FALSE
## 885 TRUE FALSE
## 886 TRUE FALSE
## 887 TRUE FALSE
## 888 TRUE FALSE
## 889 FALSE TRUE
## 890 TRUE FALSE
## 891 TRUE FALSE
## 892 FALSE TRUE
## 893 TRUE FALSE
## 894 TRUE FALSE
## 895 TRUE FALSE
## 896 TRUE FALSE
## 897 FALSE TRUE
## 898 TRUE FALSE
## 899 TRUE FALSE
## 900 TRUE FALSE
## 901 TRUE FALSE
## 902 TRUE FALSE
## 903 TRUE FALSE
## 904 FALSE TRUE
## 905 TRUE FALSE
## 906 TRUE FALSE
## 907 TRUE FALSE
## 908 TRUE FALSE
## 909 TRUE FALSE
## 910 TRUE FALSE
## 911 TRUE FALSE
## 912 TRUE FALSE
## 913 TRUE FALSE
## 914 TRUE FALSE
## 915 FALSE TRUE
## 916 TRUE FALSE
## 917 TRUE FALSE
## 918 TRUE FALSE
## 919 TRUE FALSE
## 920 TRUE FALSE
## 921 TRUE FALSE
## 922 TRUE FALSE
## 923 TRUE FALSE
## 924 TRUE FALSE
## 925 TRUE FALSE
## 926 TRUE FALSE
## 927 TRUE FALSE
## 928 TRUE FALSE
## 929 TRUE FALSE
## 930 TRUE FALSE
## 931 TRUE FALSE
## 932 TRUE FALSE
## 933 TRUE FALSE
## 934 FALSE TRUE
## 935 TRUE FALSE
## 936 TRUE FALSE
## 937 TRUE FALSE
## 938 TRUE FALSE
## 939 FALSE TRUE
## 940 TRUE FALSE
## 941 TRUE FALSE
## 942 TRUE FALSE
## 943 TRUE FALSE
## 944 TRUE FALSE
## 945 TRUE FALSE
## 946 TRUE FALSE
## 947 TRUE FALSE
## 948 TRUE FALSE
## 949 FALSE TRUE
## 950 TRUE FALSE
## 951 TRUE FALSE
## 952 TRUE FALSE
## 953 TRUE FALSE
## 954 TRUE FALSE
## 955 TRUE FALSE
## 956 TRUE FALSE
## 957 TRUE FALSE
## 958 TRUE FALSE
## 959 TRUE FALSE
## 960 TRUE FALSE
## 961 TRUE FALSE
## 962 TRUE FALSE
## 963 TRUE FALSE
## 964 TRUE FALSE
## 965 FALSE TRUE
## 966 FALSE TRUE
## 967 TRUE FALSE
## 968 TRUE FALSE
## 969 TRUE FALSE
## 970 TRUE FALSE
## 971 TRUE FALSE
## 972 TRUE FALSE
## 973 TRUE FALSE
## 974 TRUE FALSE
## 975 TRUE FALSE
## 976 TRUE FALSE
## 977 TRUE FALSE
## 978 TRUE FALSE
## 979 TRUE FALSE
## 980 TRUE FALSE
## 981 TRUE FALSE
## 982 TRUE FALSE
## 983 TRUE FALSE
## 984 TRUE FALSE
## 985 TRUE FALSE
## 986 TRUE FALSE
## 987 TRUE FALSE
## 988 TRUE FALSE
## 989 TRUE FALSE
## 990 FALSE TRUE
## 991 TRUE FALSE
## 992 TRUE FALSE
## 993 TRUE FALSE
## 994 TRUE FALSE
## 995 TRUE FALSE
## 996 TRUE FALSE
## 997 TRUE FALSE
## 998 TRUE FALSE
## 999 TRUE FALSE
## 1000 TRUE FALSE
We could manually run the first stage model, generate predicted tutoring and then use those predicted values in the second stage model like we did in the instrumental variables example, but that’s tedious and nobody wants to do all that work. We’ll use iv_robust() from the estimatr package instead.
Note: be careful! if there are missing values (in D), you may fail to replicate the fuzzy effect by hand sum(is.na(crab_data$fished)) #ok for the simulated data
Instead, we need to run a 2SLS model that includes our instrument in the first stage, which will then remove the endogeneity built into participation in the program. We’ll estimate this set of models:
##NEED TO FINISHED - IS THIS RIGHT??? \[ \begin{aligned} \widehat{\text{Fished}} &= \gamma_0 + \gamma_1 \text{Size}_\text{centered} + \gamma_2 \text{Below cutoff} + \omega \\ \text{Fishing Mortality} &= \beta_0 + \beta_1 \text{Size}_\text{centered} + \beta_2 \widehat{\text{Fished}} + \epsilon \end{aligned} \]
We can also use nonparametric methods to measure the size of the fuzzy gap at the cutoff. We’ll use rdrobust(). T
To do fuzzy estimation with rdrobust(), use the fuzzy argument to specify the treatment column (or fished in our case). Importantly (and confusingly! this took me waaaaay too long to figure out!), you do not need to specify an instrument (or even create one!). All you need to specify is the column that indicates treatment status—rdrobust() will do all the above/below-the-cutoff instrument stuff behind the scenes for you.
##NEED TO FINISHED WITH IV CREATED AS ENTRANCE EXAM
rdrobust(y = crab_data$fishing_mortality, x = crab_data$size_centered,
c = 0, fuzzy = crab_data$fished) %>%
summary()
## Fuzzy RD estimates using local polynomial regression.
##
## Number of Obs. 1000
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 481 519
## Eff. Number of Obs. 170 207
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 15.916 15.916
## BW bias (b) 27.226 27.226
## rho (h/b) 0.585 0.585
## Unique Obs. 481 519
##
## First-stage estimates.
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.055 0.102 -0.538 0.591 [-0.254 , 0.145]
## Robust - - -0.208 0.835 [-0.257 , 0.207]
## =============================================================================
##
## Treatment effect estimates.
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 16.226 7.058 2.299 0.022 [2.392 , 30.060]
## Robust - - 1.453 0.146 [-4.192 , 28.216]
## =============================================================================
That’s all! Using nonparametric methods, with a triangular kernel and a bandwidth of ±12.96, the causal effect of the tutoring program for compliers in the bandwidth is 9.683.
We can (and should!) do all the other nonparametric robustness checks that we talked about in the regression discontinuity example, like modifying the bandwidth (ideal, half, double) and messing with the kernel (uniform, triangular, Epanechnikov) to see how robust the finding is. But again, we won’t do any of that here.
https://dimewiki.worldbank.org/Regression_Discontinuity
the MixTape by Scott Cummingham: https://mixtape.scunning.com/06-regression_discontinuity
RDD with interactions: https://www.jepusto.com/rdd-interactions/
Modified from the MixTape by Scott Cummingham: https://mixtape.scunning.com/06-regression_discontinuity
library(tidyverse)
# simulate the data
dat <- tibble(
x = rnorm(1000, 50, 25)
) %>%
mutate(
x = if_else(x < 0, 0, x)
) %>%
filter(x < 100)
# cutoff at x = 70, no jump
dat <- dat %>%
mutate(
D = if_else(x > 70, 1, 0),
y1 = 25 + 0 * D + 1.5 * x + rnorm(n(), 0, 20)
)
ggplot(aes(x, y1, colour = factor(D)), data = dat) +
geom_point(alpha = 0.5) +
geom_vline(xintercept = 70, colour = "grey", linetype = 2)+
stat_smooth(method = "lm", se = F) +
labs(x = "Test score (X)", y = "Potential Outcome (Y1)")
## `geom_smooth()` using formula = 'y ~ x'
## simulate the discontinuity
dat <- dat %>%
mutate(
y2 = 25 + 40 * D + 1.5 * x + rnorm(n(), 0, 20)
)
# figure
ggplot(aes(x, y2, colour = factor(D)), data = dat) +
geom_point(alpha = 0.5) +
geom_vline(xintercept = 70, colour = "grey", linetype = 2) +
stat_smooth(method = "lm", se = F) +
labs(x = "Test score (X)", y = "Potential Outcome (Y)")
## `geom_smooth()` using formula = 'y ~ x'
# simultate nonlinearity
dat <- tibble(
x = rnorm(1000, 100, 50)
) %>%
mutate(
x = case_when(x < 0 ~ 0, TRUE ~ x),
D = case_when(x > 140 ~ 1, TRUE ~ 0),
x2 = x*x,
x3 = x*x*x,
y3 = 10000 + 0 * D - 100 * x + x2 + rnorm(1000, 0, 1000)
) %>%
filter(x < 280)
ggplot(aes(x, y3, colour = factor(D)), data = dat) +
geom_point(alpha = 0.2) +
geom_vline(xintercept = 140, colour = "grey", linetype = 2) +
stat_smooth(method = "lm", se = F) +
labs(x = "Test score (X)", y = "Potential Outcome (Y)")
## `geom_smooth()` using formula = 'y ~ x'
ggplot(aes(x, y3, colour = factor(D)), data = dat) +
geom_point(alpha = 0.2) +
geom_vline(xintercept = 140, colour = "grey", linetype = 2) +
stat_smooth(method = "loess", se = F) +
labs(x = "Test score (X)", y = "Potential Outcome (Y)")
## `geom_smooth()` using formula = 'y ~ x'
–>
We can check the size two different ways: parametrically (i.e. using lm() with specific parameters and coefficients), and nonparametrically (i.e. not using lm() or any kind of straight line and instead drawing lines that fit the data more precisely). We’ll do it both ways.
First we’ll do it parametrically by using linear regression. Here we want to explain the variation in final scores based on the entrance exam score and participation in the tutoring program:
\[ \text{Exit exam} = \beta_0 + \beta_1 \text{Entrance exam score}_\text{centered} + \beta_2 \text{Tutoring program} + \epsilon \]
Instead of using linear regression to measure the size of the discontinuity, we can use nonparametric methods. Essentially this means that R will not try to fit a straight line to the data—instead it’ll curve around the points and try to fit everything as smoothly as possible.
The rdrobust() function makes it really easy to measure the gap at the cutoff with nonparametric estimation. Here’s the simplest version: